Toretto's Market & Cafe was owned and maintained by the Toretto family, specifically Mia and Dominic Toretto. During Brian O'Conner's time as an undercover cop in the collaborative LAPD and FBI operation that suspected Dominic, Brian spent the last three weeks staking the place out under the name Brian Earl Spliner. He ordered tuna sandwiches that were considered awful by those who frequented the market, including Mia, who suspected Brian's ulterior motives for visiting the market.
It is assumed Mia still ran the market for a living while she continued to live in Los Angeles. However, it was presumably shut down or sold when she and Brian helped Dominic escape incarceration and subsequently fled Los Angeles. The market is never mentioned nor does it appear in any films following The Fast and the Furious.