Harrison, slated to be the No. 2 starter in the Rangers' rotation behind Yu Darvish, has persistent inflammation in the second toe on his left foot.
Rangers spokesman John Blake said the 27-year-old left-hander will try to throw a bullpen session Sunday and could return to Texas to be examined by orthopedist Dr. John Crates.
"We want to nip this in the bud and find out what we have," Rangers manager Ron Washington said. "We've got plenty of time. We'll know where we are when he gets back from the doctor."
Texas first baseman Mitch Moreland also sat out with a tight right quadriceps and is day to day.
Kyle Blanks had a two-run homer for the Padres and is hitting .393 (11 for 28). Blanks, who has two exhibition homers this year, is trying to bounce back from a series of long-term injuries that limited him to 40 games in the last three seasons.
Blanks had right elbow ligament-replacement surgery in 2011 and missed all but 20 games of last year after tearing a labrum in April. He has 88 home runs in parts of seven minor league seasons in the organization.
"Guys like Blanks who are coming back from injuries have to get back on the field and play, and this spring is a great opportunity for them," Padres manager Bud Black said.
San Diego starter Eric Stults allowed three runs -- two earned -- and five hits in three innings, giving up Allen's long homer to left field. Slated for the back end of the rotation, the 33-year-old left-hander has allowed eight earned runs in seven innings over three outings.
"I felt comfortable throwing to the arm side of the plate and I got a lot of ground balls," Stults said. "The biggest struggle today was glove-side fastballs. I left a couple up, especially that home run to Allen. But overall, today was the best I've felt on the mound."
Rangers 3B Mike Olt made back-to-back nice plays to throw out Jesus Guzman and Jedd Gyorko in the second inning. ... With seven players ain the World Baseball Classic and split squads, the Rangers filled their travel roster with minor leaguers.