Atlanta placed Smith on injured reserve Saturday, Scott Bair of the team's official site reports.
Smith (ankle) is listed as doubtful ahead of Sunday's contest against the Colts, Michael Rothstein of ESPN.com reports.
Smith played 10 of 52 snaps on offense and went without a carry or target in Sunday's 9-7 loss to the Panthers.
Smith (concussion) was not listed on Atlanta's injury report Thursday.
Smith (concussion) practiced in full Wednesday, Amna Subhan of the Falcons' official site reports.
Smith (concussion) has been ruled out for Sunday's game against the Vikings, Josh Kendall of The Athletic reports.
Smith (concussion) has been ruled out for the rest of Sunday's game against the Titans, Michael Rothstein of ESPN.com reports.
Smith caught his only target for 28 yards during Sunday's 21-19 win over the Texans.
Smith played 29 snaps (10 offensive) and recorded an assisted tackle during Sunday's 24-10 win over the Panthers.
The Falcons re-signed Smith on Monday, Greg Auman of Fox Sports reports.