Simon retired his first 14 batters before Desmond Jennings singled with two outs in the fifth and struck out three.
Miguel Cabrera hit his third home run of the spring, doubled and drove in three runs in an 11-5 loss to the Tampa Bay Rays.
Tigers manager Brad Ausmus said he expects Verlander to follow David Price in the rotation and pitch the second game of the season.
Acquired from Cincinnati after going 15-10 last season, Simon gave up five hits, walked three and struck out two.
Cabrera was playing in his sixth game of the spring while recovering from offseason surgery on his right ankle.
Verlander believes not drinking enough water before the game and a further arm extension from his revised mechanics may have contributed to the cramping.
“I have work to do on my slider,” Verlander said. “My slider has been about 50-50.
Price struggled, allowing eight hits and two runs in 4.1 innings, while also walking a batter, striking out seven and stranding seven baserunners.
Both are expected to be designated hitters in Sunday’s split-squad games with Martinez going to Kissimmee to face the Atlanta Braves and Cabrera staying at home against the Washington Nationals.
Alfredo Simon allowed six first-inning runs before settling down with two shutout innings. Joe Nathan, Joba Chamberlain and Joakim Soria also pitched scoreless inning for the Tigers.