Outfielder Juan Gonzalez has a strained left hamstring.
"He wasn't going to play today for sure," manager Eric Wedge said after Wednesday's game against the New York Yankees was rained out.
"Juan felt some tightness and I won't really know a lot more until he gets out there on a good day and gives it a try," Wedge said.
"Obviously, we were hoping something like this wouldn't happen. We need to see him on a constant basis."
Gonzalez, 35, is back with Cleveland after three injury-plagued seasons with the Texas Rangers and Kansas City Royals.
He played only 33 games last year for the Royals and none after May 22 because of strained back. A right thumb injury limited him to 70 games with Texas in 2002 and a right calf injury cut short his 2003 season with the Rangers after 82 games.
"It's still early and this doesn't jeopardize things, but we've got to get him healthy and back out there," Wedge said.
Gonzalez hit .325 with 35 homers and 140 RBI for the Indians in 2001 before signing as a free agent with Texas.