Can I freeze tzatziki sauce?

I haven't tried it, but I don't see why not. Sure, cucumbers have a lot of water, but you're already crushing them in a blender or processor to make the sauce, so you don't have to worry about bursting cell membranes.

I suppose if you made some kind of chunky tzatziki, you might be concerned about a change in texture. I've never seen a chunky tzatziki (and it doesn't sound very appetizing, IMO) but searching Google, I found mixed advice on this subject. Some of the recipes I found call for finely chopping or mincing the cucumbers and in that case I can see why you might have some issues.

Globalpost.com has this advice on a page called, appropriately, How to Freeze Tzatziki:

You can freeze extra tzatziki for later use, but don't expect perfect results as you might with foods such as lemon curd. Cucumbers usually become mushy when frozen, but the acidity in yogurt does protect some of the original crunch. Yogurt fares better in the freezer, but some liquid separation can occur and it might taste more acidic when thawed. You can stir the liquid into the tzatziki sauce after it thaws, but it might not be as smooth.

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If the cucumbers become too mushy in the thawed tzatziki, you can strain them out of the yogurt and stir in fresh cucumbers.

My advice would be, try to puree your cucumbers really finely for sauce that you intend to freeze, to minimize any change in texture.

I wouldn't freeze tzatziki sauce.

Dairy practically never freezes well. It is a fat-water emulsion, and it is likely to change its structure a lot upon thawing. You have to prepare it and stabilize it a lot, and then also preferably use a special freezing method (such as making ice cream with agitated freezing).

The other part are the cucumbers, which are a fresh vegetable. There is no way they will keep their texture. Of course you can freeze vegetables if you don't mind them softening, but the point of tzatziki is that the pieces of cucumber crunch when you bite on them. Cucumbers taste so mild, especially when diluted in yogurt and overpowered by dill and garlic, that they contribute nothing but texture.

So, altogether, it's a poor candidate for freezing. And besides pickling, I don't think there is another way to preserve cucumbers well - whatever you do, they will lose texture. Keeping them as puree or juice doesn't make much sense, you can use water instead for all the taste you'll get out of it.

I froze shredded cucumbers and used them a month later in tzatziki sauce. It turned out wonderful! First, I peeled and removed all cucumber seeds. Second, I shredded them. Third, I salted them and let them rest in my colander for about a half hour. Finally, I squeezed out as much water out as possible with paper towels. I placed them in Ziploc bag and removed the air inside and froze them. I made fresh sauce yesterday but I did not add more salt to the final recipe. Once my cucumbers thawed, they still had enough juice (not too much) for the sauce.