The Cavs said Love will get treatment and rehab the injury but will not be reassessed until "approximately three to four weeks."
Love missed the team's season opener because of the injury, played 38 minutes in the Cavs' second game, a 128-119 double-overtime victory at Detroit, and played just nine minutes in the third game before leaving.
The five-time All-Star is averaging 9.5 points, 6 rebounds and 2.5 assists this season.
Before the game against the Pistons, Love said he had gotten kicked in the leg earlier this month in a preseason game against Indiana and that the injury had caused swelling throughout his calf and down to his Achilles tendon.
With Love out, coach J.B. Bickerstaff will likely put Larry Nance Jr. back in the starting lineup. Nance started the opener.
Love is in his seventh season with Cleveland, which is counting on him to lead a young team that is showing early signs of growth this season. He has averaged 18.2 points and 11.1 rebounds in his career since breaking in with Minnesota in 2008.
Cleveland (3-0) will play the New York Knicks (1-2) on Tuesday night.
The Associated Press contributed to this report.