Articles with Spatial Prepositions

The second sounds wrong to me, because it sounds like you're using a with a plural. Of course walk is actually singular.

She lives two minutes' walk from the station

She lives a two-minute walk from the station

According to Which is correct use of the apostophe in minutes? a two-minutes' walk is not wrong.

It is the one without the article that is correct:

She lives two minutes' walk from the station.

Discussion

The phrases in boldface below are called measure genitives, or, alternatively, genitives of measure (Longman, p. 296, which where the four examples below come from):

Perhaps he took my thousand dollars and put me to skep with two dollars' worth of ether.
Their huts were 12 hours' journey from the nearest main road.
I want ten years' supply of whisky.
I held the telephone at arm's length and stared at it.

As is clear already from the first three examples, when a cardinal number precedes the noun in the genitive, we generally don't need another determiner in front.

This doesn't mean, however, that we may never put another determiner in front. Consider the following examples from CGEL (p. 470):

a second [one hour's delay]
the [one dollar's worth of chocolates] he bought

Arguably, the following are also acceptable: a second [two hours' delay], the [two dollars' worth of chocolates] he bought. CGEL says that these examples show that measure genitives are attributive modifiers rather than determiners, because in these examples they actually follow a determiner (immediately or with an intervening adjectival attribute). CGEL further says that

When they occur in this position, i.e. after a determiner, they are subject to the constraint described in §6.2, so that the indefinite article is dropped: instead of ^*this [an hour's delay] we have this [hour's delay]. In this case the measure genitive (hour's) has the status of a nominal, but otherwise measure genitives are full NPs (noun phrases).

Because they are modifiers not determiners, measure genitives do not confer definiteness on the NP. While a friend's dog, with Type 1 genitive, is definite ("the dog of a friend"), an hour's delay is indefinite ("delay of an hour"). Nor can they occur initially with nouns that require a count interpretation: ^*We played [an hour's game of squash]; instead we need the compound adjective construction We played a [ one-hour game of squash].

If the last sentence is correct, by the way, it implies that walk is used as an uncountable noun in your example. This is rather extraordinary, because I certainly can't think of another construction where walk is uncount. For example, ^*I had/did lots of walk today doesn't work. Moreover, among the major dictionaries that explicitly state whether a given sense of a noun is count or uncount (Cambridge, Collins, and Macmillan), none of them record an uncount sense for the noun walk. Nevertheless, postulating that walk is uncount in two minutes' walk does have the advantage of making it unsurprising that no determiner is needed in front; after all, count nouns in the singular normally require a determiner, whereas uncount nouns in the singular do not require one as long as they are indefinite. The disadvantage is that walk is not the only noun for which we need to postulate this unique uncount sense: we have to do the same with dollar and arm, for example.

As usual, analyzing grammatical rules that someone wrote down is actually not decisive as far as whether a given construction is acceptable or not. What we need to do is look at actual patterns of usage among native speakers. So, let's verify that the article is indeed missing in reputable sources such as published books. This is indeed so: see the numerous examples here and here. Here and there we find usage with an article (e.g. here), but that is very rare by comparison.