Klesko also had a cortisone shot in the same shoulder in January.
Klesko's symptoms are similar to those he experienced in his right shoulder prior to surgery in 2004.
"We know he has some arthritic changes in there," trainer Todd Hutcheson told the San Diego Union-Tribune of Klesko's shoulder. "We know it's going to be sore from time to time."
Klesko's shoulder problem could be good news for reserve first baseman Adrian Gonzalez, who is on the bubble between sticking with the Padres and opening the season with Triple-A Portland.
Even before Klesko's recent problems, the Padres had been considering keeping Gonzalez -- who is the heir apparent at first when Klesko's contract runs out at the end of this season -- as a late-inning defensive replacement.
It is becoming clear that a starting pitcher or two will open the season in the Padres' bullpen.
Which means the fourth starter will come from the trio of Brazelton, who has been the Padres' sharpest starter this spring, Williams and Park. The last two will be in the bullpen.
The Padres are leaning toward Brazelton winning the fourth spot in the rotation on merit. As for the bullpen, Park served as South Korea's closer (three saves in four appearances) in the World Baseball Classic.
Appearing in a relief role Tuesday, right-hander Dewon Brazelton might have clinched his berth in the Padres rotation.
Brazelton worked out of a bases-loaded situation when he took over in the fourth for starter Chan Ho Park against the Angels. The former Devil Ray allowed no runs on one hit in 3 1/3 innings to lower his exhibition ERA to 1.17.
The outing was Brazelton's last of the spring.
Park, meantime, gave on six runs (five earned) on 12 hits in 3 2/3 innings as his post-World Baseball Classic spring ERA climbed to 9.39. The third candidate for the last two starting jobs in the Padres rotation is Woody Williams, who has a 6.55 ERA.