Smith said Wednesday that Grimes has been playing with a sore knee since the Falcons' win over Detroit on Oct. 23. He left Sunday's victory over Minnesota in the first quarter.
"He's been doing everything in his power to get back out on the field," Smith said. "He's been playing with it. Right now, he will be out for a couple of weeks. He's going to have a minor procedure done on his knee. We don't know the time frame in terms of getting him out. Brent's been fighting through it for some time."
The Falcons are thin at cornerback for this week's game at Houston.
Smith says nickel back Kelvin Hayden is "probably very doubtful" after missing the Minnesota game with a toe injury.
Darrin Walls likely will be active for the first time this season.
Smith says he hopes linebacker Stephen Nicholas (quadriceps) can return to practice late in the week.
Pat Yasinskas covers the NFC South for ESPN.com. Information from The Associated Press contributed to this report.