"We anticipate John will be back out practicing with us before the end of the week," Smith said Monday, via Pat Yasinskas of ESPN.com.
Abraham aggravated his sprained ankle during the second quarter of Atlanta's thrilling Divisional round win over the Seattle Seahawks, and did not return to the game.
Abraham originally sprained his ankle in Atlanta's Week 17 loss to the Tampa Bay Buccaneers -- a meaningless game in terms of playoff seeding, as the Falcons clinched home field advantage in Week 16.
Though injured yesterday, Abraham vowed to reporters that he'll suit up and take the field next Sunday, when the Falcons host the 49ers with a trip to Super Bowl XLVII on the line.
During the regular season, Abraham appeared in all of Atlanta's 16 games, recording 35 tackles, registering 10 sacks and forcing six fumbles.
Kickoff between the Falcons and 49ers is scheduled for 3 p.m. on Sunday.