Smith, 35, wore the brace to keep his leg in place after he broke it last season.
"The last eight months have been nothing short of crazy," Smith's wife Elizabeth Smith wrote on Instagram. "Although it's not over, today is a big milestone.
"We are shedding the weight Alex has been carrying [literally and figuratively]. It's one step closer to the goal. The resilience, determination and mental fortitude of this man is unmatched."
Smith led the Redskins to a 6-4 record while throwing 10 touchdowns against five interceptions to start his 2018 campaign. He sustained a broken fibula and tibia in a game against the Houston Texans on Nov. 18.
He is not expected to play in 2019. The Redskins have since acquired veteran quarterback Case Keenum in a trade and used a first round pick on former Ohio State quarterback Dwayne Haskins in the 2019 NFL Draft.
Smith attended Redskins workouts this off-season and was seen throwing passes, but the quarterback says he needs to learn to run again.
"I've got to conquer some more steps before I get there," Smith told Fox 5 DC in June. "Learn to run again. That's a big one. I'm already throwing.
"I already feel like throwing is not a problem. I feel like I can throw. But dropping, moving around, all that kind of stuff, change of direction."
Smith said he plans to play football again.