Does cyberpunk exclude interstellar space travel?

No, I would say it does not. Walter Jon Williams' Voice of the Whirlwind (1987) is the sequel to Hardwired (1986), one of the prototypical cyberpunk books of the first wave of cyberpunk. It features most of the standard cyberpunk tropes: used future, corporate takeover of public goods, neural implants, "street" culture, bootleg technology, etc.

Voice of the Whirlwind takes place in and around Earth, but the main character, Steward, was previously a soldier deployed to a corporate colony in another star system, where he fought in a war against other corporations until the planet's owners, The Powers, came home and kicked the human corporations out.

The Powers have basically restricted humanity to the solar system (in the story's present) but have 2 stations in the asteroid belt for commercial and political dealings. So in this setting interstellar travel is definitely possible, and humans have done it. I don't recall any description of how it works, so it may be sub-light.

Wikipedia describes Cyberpunk as:

a subgenre of science fiction in a dystopian futuristic setting that tends to focus on a "combination of low-life and high tech"1 featuring advanced technological and scientific achievements, such as artificial intelligence and cybernetics, juxtaposed with a degree of breakdown or radical change in the social order.

From this, and looking at my exposure to Cyberpunk (Blade Runner, and Neuromancer) it sounds like the genre doesn't necessarily exclude interstellar travel, so long as it isn't ubiquitous for everyone freely. That level of freedom means it's no longer dystopian. But it's still possible with 'advanced technological and scientific achievements'.

As a concrete example, the Tears in Rain speech from Blade Runner (undeniably cyberpunk) references the "Shoulder of Orion," which would either be Betelgeuse or Bellatrix, objects well out of our solar system.

The end of Neuromancer references:

So no Cyberpunk doesn't need to exclude interstellar travel, but it's often not a common component as the ubiquity of it would not be dystopian.

Cyberpunk and interstellar travel can coexist; the key aspect to make these styles compatible is that the future remains "unevenly distributed": Despite there being very high technology, there are still people living at a low end of the socioeconomic spectrum, using bits and pieces of equipment cast off by the richer strata (or supplied by members of the upper crust who are running their own side-plots and use folks on the street as tools).

Catspaw, by Joan D. Vinge, is a good example of a book that combines strong cyberpunk feel with an interstellar society in this way.

A second example is the story The Detective's Tale: "The Long Good-Bye" from Hyperion by Dan Simmons, which builds a cyberpunk narrative into a world that (as experienced by characters in other stories from the book) has aspects more often associated with other science fiction genres, including interstellar travel by both spaceship and teleportation gate. The gates are directly incorporated into the plot of this story.

Bruce Sterling's Machinist/Shaper universe is often cited as cyberpunk. Most of the characters are aggressively venal and greedy in their pursuit of power, the aliens are motivated by a compulsive capitalist ethos and there is a hefty dose of skepticism about mankind's ability to achieve lasting contentment or peace in an increasingly technology driven society.

While the bulk of the action takes place in the solar system (although they have definitely made it to the asteroid belt) we see a number of interstellar embassies and the investors represent an extra-solar faction. Further, the ending of Schismatrix suggests more mysterious fields of exploration for Abelard Lindsay.

Cyberpunk does not exclude interstellar or intergalactic travel.

In cyberpunk, the dystopia is primarily from a society having an extreme socioeconomic imbalance; and the protagonists are either metaphorical or literal outsiders within their societies. (In Gibson’s Neuromancer, the protagonists were mercenary criminals; Altered Carbon, a body-swapping terrorist.) The ability to travel to another planet does not mean that economic problems would vanish and a post-scarcity society would form (as in Star Trek), or that people would not be exploited, be left outside society or want to stand apart from society. The social and economic relationship between colonial and core worlds, how communication and travel is done, and what entity is doing the colonising for what reason, and the societies and cultures of the colonies, could all create a cyberpunk culture (either a dominant one or subculture(s)).

I think in an interstellar setting, “cyberpunk” could form subcultures (eg, a population of a failing colony planet, the attitude of some interstellar economic migrants) rather than an overall ethos and theme. An early edition of the hard science-fiction TTRPG Traveller may have used this approach for some planet settings. And the TTRPG Cyberpunk 2020 (which Cyberpunk 2077 and Cyberpunk Red are sequels of), also featured interplanetary travel.

As well as the usual cinematic picks for cyberpunk (Blade Runner, Minority Report, Ghost in the Shell), you can also see elements of how cyberpunk could work in an interplanetary scale in Alien, The Expanse (TV version) and Firefly. All of those feature thematic elements that could appear in a cyberpunk setting, but do not have the accepted aesthetics.

A number of the other answers have made good cases for why cyberpunk can include interstellar travel and provided good examples.

But what is it, exactly, that can keep things cyberpunk in space? In my observation, one of the key elements of cyberpunk is that there is never any real escape. The controlling systems and organizations of the civilization are pervasive, and whether you're deep in a crowded city or out in some polluted wasteland, you're never far from the reach of the powers that be.

When space and interstellar travel create an open frontier and wide separations, that feeling of claustrophobia and control vanishes, and you end up with works that are not cyberpunk. But the physical scale and distances don't matter if people are still tightly linked by data and the same organizations extend their control across the stars. I find Altered Carbon to be a particularly clear example of this: anybody can easily travel between star systems, but that just means that all those far-flung locations seem as though they are part of the same big grungy city.

In short: in interstellar cyberpunk, maybe anybody can leave the crummy Earth, but the rest of the universe is still part of the same crummy system.