Kamaroŭski market, or Kamaroŭka, is the main grocery destination in Minsk. It has an outdoor section where you can find fresh seasonal fruits and vegetables. High-quality meet chops, homemade cheese, cottage-cheese and milk are in the indoor section. Kamaroŭka also offers pre-cooked foodstuffs in several bistros (Belarusian and Arab dishes), including take-away food. Those who like Oriental tastes can order kebab/shawarma, pilaw, spicy soups and even falafel (one Arab cook made wonders to get it certified by the city’s public health office).
The most popular among bistros here is called "Oriental Express" (Vostochnyi Express) and offers huge and tasty portions for $5-6 each.
Vietnamese fast foods often called Saigon or Hanoi are also popular with some Minskers. Located in the suburban markets, they attract regular clientele. It is up to you but perhaps you could look for safer options.