The Rangers announced after Sunday's 7-3 win over the Boston Red Sox that the right fielder will travel with the team and be re-evaluated Monday.
"I feel good," Cruz said Sunday morning. "I don't feel anything, but I don't want to take a chance today."
While Cruz remains on the active roster, starting pitcher Rich Harden wasn't so fortunate, as the Rangers placed him on the 15-day disabled list with right shoulder tendinitis.
Harden, who lasted just 2 1/3 innings in his last start, was slated to pitch Tuesday at Tampa Bay after having his weekend start pushed back. Harden is expected to begin a rehab stint on Tuesday with Triple-A Oklahoma City.
Tommy Hunter, who was knocked out of Friday's start in the fourth inning, will move up a day and start Tuesday. Derek Holland, who has been on a rehab assignment, confirmed to ESPN 103.3 FM's Ben & Skin Show on Monday that he'd start vs. the Rays on Wednesday.
The Rangers said after Hunter was pulled Friday that he had been affected by a stomach bug.
Cruz, who his hitting .320 with 16 homers and 64 RBIs in 77 games, has already made trips to the disabled list twice this season with strains in each of his hamstrings. Cruz said it didn't feel as severe this time.
The Rangers, however, are remaining cautious.
"His strength is better today than it was when he left last night, but once again we're talking hamstring and we're going to make sure that this thing don't get worse," Rangers manager Ron Washington said before Sunday's game. "So we definitely have to make a decision. We're just going to wait for the medical staff to finish their evaluation on everything and see what happens."
Cruz said he felt tightness prior to and during Saturday's game. After he sent a line drive off the wall in the seventh inning, Cruz slowed as he rounded second base on his way to a triple. He left the game after the inning.
Rookie Mitch Moreland, who has been playing first base since his call-up, got his first start in right field Sunday in place of Cruz.
In other roster moves, outfielder Brandon Boggs was recalled and was in uniform for Sunday's game.
Jeff Caplan covers the Rangers for ESPNDallas.com.