Manager Terry Francona said Cabrera could miss three to four weeks, although he said that's merely a guess.
Cabrera had to be helped off the field Monday night at Yankee Stadium after hurting himself running out a grounder. He returned to Cleveland for an MRI.
"This is where the versatility of the club should help us," Francona said.
Cabrera is hitting .254 with five home runs, 25 RBIs and a team-leading 18 doubles. He also has a 32-game errorless streak despite playing the last few weeks with quad problems.
The 27-year-old Cabrera made the AL All-Star team in each of the last two seasons. He hit .270 with 16 homers and 68 RBIs last year.
Cabrera went on the DL with Cleveland trailing Detroit by one game in the AL Central.
The 24-year-old Diaz made his big league debut with Cleveland last year and played five games. He was hitting .211 with four homers and 18 RBIs at Triple-A this season.
Diaz has only played shortstop in the last seven seasons, but recently has been taking grounders at second base.