Darvish exited in the third inning. The right-hander didn't look comfortable on the mound and was pulled after throwing a ball in the dirt to Josh VanMeter.
San Diego manager Jayce Tingler wouldn't speculate about whether Darvish will make his next scheduled start and said the team will see how he responds to treatment.
"Long, frustrating game tonight for sure," Tingler said.
Darvish (7-7) gave up five runs on six hits and a walk through 2⅔ innings. He struck out four and threw 74 pitches.
If he were to miss significant time, it would provide another obstacle for the Padres as they try to climb in the National League West standings. They're in third place, nine games behind the first-place San Francisco Giants and five back of the Los Angeles Dodgers. San Diego currently holds the second NL wild-card spot.
The Padres already have several important players on the injured list, including star shortstop Fernando Tatis Jr., infielder Jurickson Profar, and pitchers Drew Pomeranz, Dinelson Lamet and Chris Paddack.
Suddenly, the team's playoff chances look tenuous.
"We don't have time to feel sorry for ourselves or anything like that," Tingler said. "This is what we've got. This is baseball. Everyone deals with some type of adversity. We've got to continue to fight and battle."
The Associated Press contributed to this report.