Smith was diagnosed Wednesday with a low-ankle sprain and is considered week-to-week, Ian Rapoport of NFL Network reports.
A high-ankle sprain would have necessitated a longer recovery timeline, but Smith's low-ankle injury looks as though it'll still be enough to keep him on the sideline for one game. He suffered the injury in Sunday's overtime loss to the Packers, playing just 17 snaps before departing. Though Smith has turned in only seven receptions for 58 yards on 11 targets through four games, his absence should at least clear the way for Hunter Henry to absorb a larger share of the snaps and targets available at tight end. New England doesn't currently have another healthy tight end on the roster beyond Henry, so expect the team to add a body to the position group in advance of this weekend's game against Detroit.