Also, Cavs rookie Sergey Karasev has left the team to obtain his work visa. He is expected to be back for Thursday's game against Detroit.
The team announced the injuries Monday following coach Mike Brown's media availability. The Cavs host the Charlotte Bobcats on Tuesday in Canton, Ohio.
Jack, who signed with Cleveland as a free agent, has irritation on the underside of his patella tendon, the team said in a release.
With the Oct. 30 opener approaching, the Cavs have some injury issues. Center Andrew Bynum remains sidelined as he works on his knees and forward Tyler Zeller is out after having his appendix removed and hurting his hip.