Darvish (10-7, 3.06 ERA) reported tightness in his right elbow while playing catch on Monday and was examined by team doctor Keith Meister on Tuesday night.
Rangers general manager Jon Daniels said an examination of Darvish's elbow reported no ligament damage, however he will undergo a MRI on Thursday.
Daniels said Darvish has some tightness in his pronator flexor muscle and is expected to miss two starts.
"We're going to get a MRI to be certain," Daniels said prior to the Rangers game against the Tampa Bay Rays. "I think Yu had expressed he could pitch if we're in a different spot, a meaningful game tomorrow, Yu would be game to go. But we all agreed, he agreed, we all agreed, it better to be cautious. We're hoping it's a two-start DL."
In Darvish's last start on Saturday, he lasted just four innings, allowing six runs, five earned while throwing 113 pitches in a loss to the Houston Astros.
Darvish said he didn't have any physical problems during his start.
However, Darvish reported some issues two days later and skipped a bullpen session.
While talking with reporters on Tuesday he discussed the possibility of fatigue.
"At this time of the season, you are going to be fatigued so you have to do everything you can to get back to normal," he said.
The Rangers will call up left handed Robbie Ross Jr., from Triple-A Round Rock to replace Darvish, who was scheduled to start on Thursday against Tampa Bay.
With Darvish on the DL, the team purchased the contract of left-handed reliever Alex Claudio from Triple-A Round Rock. Claudio threw a scoreless 8th inning and struck out one in the Rangers' 10-1 loss to the Rays.
This is the third time Darvish has gone to the DL in his career. He went on the DL March 21-April 5 with neck stiffness and last season he spent 15 days on DL with a right trapezius strain.
Darvish has been the lone bright spot in this terrible season for the Rangers (47-72) that field the second-worst record in baseball.
The Rangers lead the majors with 14 players currently on the DL and also have placed a major league leading 24 players on the list this season.
With Darvish going to the DL, he becomes the seventh pitcher on the list currently.
"With the year we've had with injuries, we're not going to push anything and chance it at this point," Daniels said.