The Cavaliers, who have the league's worst record at 1-10, were already playing without All-Star forward Kevin Love (toe surgery).
Cleveland's first-round pick, point guard Collin Sexton, will continue in the Cavaliers' starting lineup. He scored a team-high 15 points in a career-high 42 minutes in a loss to Oklahoma City on Wednesday night.
Hill, 32, had his best game of the season in a loss to Orlando on Monday, scoring 22 points. He was a late scratch from Wednesday's loss because of the shoulder injury.
With Hill lost for two weeks, the Cavaliers have agreed on a two-way deal with guard Andrew Harrison, league sources said. Cleveland is waiving guard John Holland, the sources said.
Harrison averaged 7.5 points for Memphis in the past two seasons before his recent release. Cleveland's plan is to keep Harrison, 24, on its NBA roster for as long as he's with the franchise; he will not be assigned to the G League.