Tallinn is European country, so selection of fruits and vegetables is mostly same as in other EU countries. Of course, during the winter there will be just few locally grown crops (potatoes, cabbage, pumpkins, onion, carrots, beet), and most are imported from southern countries like Israel, Spain, Italy and also from Asian and African countries (tomatoes, cucumbers, artichoke). If one is looking for less common (or even some exotic) vegetables then there are several large department shops in Tallinn where you can find them fresh.
Beware, that there is no culture of small street grocery markets that sell good quality fresh food. There are 2-3 food markets in the town, but vast majority of people buy food from chain shops.