Luebke won't go on the disabled list, though it's unclear when he will reappear in the starting rotation.
Jeff Suppan, 37, will be officially added to the 25- and 40-man roster before he starts Wednesday for the Padres against one of his former teams, the Brewers.
"We're going to push Cory back a few days. We're being a little cautious," Padres manager Bud Black said before Tuesday's game. "He's feeling much better. We are feeling confident that this will be just one start."
Luebke said he first noticed the tightness during his start against the Giants. He allowed two runs over six innings on his way to his third victory of the season. Luebke (3-1) has a 2.61 ERA over his five starts and has been one of the few bright spots for the 7-17 Padres.
"It's early [in the season] so we're trying to stay on top of it," Luebke said. "I've been lucky in that I have never had anything wrong with my arm. Hopefully, this will be the last of it."
In March, Luebke signed a contract extension that guarantees him $12 million and could earn him as much as $27.75 million and could keep him with the team through 2017.
Luebke has been receiving treatment on the elbow from the training staff since late Friday and said he was encouraged with the way it was feeling Tuesday afternoon.
"It feels significantly better than it felt Friday," Luebke said.