Morejon only faced three batters in the first inning, leaving after a four-pitch, two-out walk to Joey Gallo.
Craig Stammen took over for Morejon and led a parade of six effective San Diego relievers as the Padres shut out the Rangers, 2-0.
Padres manager Jayce Tingler said after Sunday's game that Morejon felt tightness on his third pitch to his final batter.
Morejon, 22, was making his second start of the season. He worked four innings at home against Arizona last Monday and allowed two runs, both on home runs, and got a no-decision in the Padres' 3-2 loss.
Morejon appeared in 14 games for the Padres during the previous two seasons, including six starts, without a decision.
The Associated Press contributed this report.