placement of "only"

It is modifying the phrase "buying fish". It is adding a condition to the act of making a purchase. I believe that is not ambiguous but conditional.

Does the placement of the "only" make the sentence ambiguous?

No, it is the lack of punctuation:

I will buy fish only, if I shop at the pier - I will buy nothing except fish if I shop at the pier.

I will buy fish, only if I shop at the pier - (there is an implied "but") I will buy fish from nowhere other than the pier