While his departures from those games were attributed to right wrist soreness and forearm tightness, general manager Chris Young said an MRI showed some inflammation in the elbow.
"There's no need to push him," Young said. "He came in today and felt OK, which is a positive, but given how important he is to us and our season, we're going to play this very cautiously and see how he responds over the next several days to treatment."
Young said the Rangers should have a pretty good idea in seven to 10 days on what the next steps would be for the two-time National League Cy Young Award winner. DeGrom was coming off two injury-plagued seasons with the New York Mets when he signed a $185 million, five-year contract with Texas in December.
The American League West-leading Rangers recalled right-handed pitcher Yerry Rodríguez from Triple-A Round Rock.
When deGrom left a game in Kansas City after four hitless innings on April 17, the Rangers said the move was precautionary because of wrist soreness.
After the right-hander left his start against the New York Yankees with two outs in the fourth inning Friday night, manager Bruce Bochy said the move was again precautionary and that deGrom had forearm tightness. Before Saturday's game, and Young's announcement, Bochy said the "same thing cramped up on" deGrom.
Young said he felt the wrist issue was different and under control.
"But was there some compensation from the wrist that maybe irritated this? Perhaps, but I can't say for certain," said Young, a former big league pitcher.
Texas has won all six games started by deGrom (2-0), but he has been limited to 30⅓ innings. He has a 2.67 ERA with 45 strikeouts and four walks.
"He's being very smart about it. He's making us aware of how he's feeling," Young said. "He wants to be out there as much as anybody. He was very disappointed last night to have to come out of the game, but he felt like he shouldn't push through and potentially make something worse than maybe it is. And I think today's information confirms that he made the right decision."
In between the two starts he left early over injury concerns, deGrom struck out 11 batters and allowed one earned run over six innings in a win against Oakland on Sunday.
DeGrom played his first nine big league seasons with the Mets. He was limited to 156⅓ innings over 26 starts the past two years.
Before missing the final three months of the 2021 season with right forearm tightness and a sprained elbow, deGrom had a career-low 1.08 ERA over 92 innings. He was then shut down late in spring training in 2022 year because of a stress reaction in his right scapula and didn't make his first big league start until Aug. 2.
Later Saturday, Nathan Eovaldi pitched a three-hitter for his first nine-inning shutout in the big leagues, Ezequiel Duran hit a two-run homer in the fifth inning and the Rangers blanked the Yankees 2-0, New York's fifth loss in seven games.