Andrews performed the original surgery in 2007 and the revision a year ago.
"We'll figure out where to go from there, maybe a visit and then see what to do," Johnson said on Monday.
Johnson, who hasn't pitched in the big leagues since 2013, first felt something in his elbow while warming up for Saturday's outing.
"But I was talking to Xavier Nady, who is the hitting coach, and I said that 'maybe some adrenaline will get it going and get through that last little hump.' It didn't really go that way," Johnson said.
Johnson described the soreness on the "outside" of the elbow and "a little on the inside."
"It's all over the place," he said. "That's never a good sign."
That said, Johnson isn't wasting time playing the 'what-if' game. He's been down this road before and has adopted a pragmatic approach to his health.
"I'm not going to jump to any conclusions," said Johnson, who will be a free agent after the season, but said he's receptive to returning to the Padres.
"Until I talk to him [Andrews] or see him, I will sit back and wait and not get down on it. It could be a bump in the road and maybe the time off in the offseason will be good."
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.