Wallace, acquired in last month's three-team trade from the Chicago Bulls, has missed two games and part of another with the injury.
With 10 regular-season games remaining, the Cavaliers want Big Ben as ready as possible for the postseason.
"We just have to make sure going down the stretch that he gets enough rest with that back so that you can limit the effects going into the playoffs," coach Mike Brown said following Tuesday's practice.
Wallace, who is averaging five points and eight rebounds since joining Cleveland, had an MRI exam on Saturday -- one day after he left in the third quarter of a win over Toronto. He also sat out a March 12 game against New Jersey when his back tightened up.
In a season of ongoing injury problems, the Cavaliers are expected to get back guard Daniel Gibson, who has been sidelined since Feb. 20 with a high left ankle sprain. Gibson went through Cleveland's entire practice on Tuesday, and Brown said the Cavaliers' training staff would decide if the second-year shooting threat would face the Hornets.
Also, the Cavaliers signed center Lance Allred to a second 10-day contract. He has appeared in two games since signing with the Cavs on March 13.