Cruz, who is hitting .270 this season with a team-best 28 home runs and 84 RBI, had an MRI scan which revealed a grade 1 strain of his left hamstring.
The 31-year-old incurred the injury while running the bases on a double in the sixth inning of the Rangers' 9-5 win over their division rivals, the Los Angeles Angels, Sunday.
"Obviously, this is another challenge," Rangers president Nolan Ryan was quoted as saying on the team's website. "We are looking at our options and seeing what we can do to fill that hole."
"Lance is having an outstanding year," Ryan added. "Is it a possibility? I guess you could say it's a remote one.
"There are other players who have cleared waivers, so it's premature for me to speculate, but if that's a possibility, we would have to give it consideration."
The Rangers lead the AL West standings by three games from the second-placed Angels.
(Writing by Mark Lamport-Stokes in Los Angeles; Editing by Frank Pingue)