Monday's outing could be a big step for Johnson, who also threw a simulated game in April and felt triceps tightness afterward, slowing his recovery a bit.
Johnson signed an incentive-laden deal with the Padres in December, based mostly on how many starts he makes with the club. He hasn't pitched in a Major League game since 2013 with Toronto.
• Making his first appearance since undergoing his second Tommy John surgery last February, left-hander Cory Luebke pitched a perfect inning for Class A Advanced Lake Elsinore on Saturday night. Luebke threw 14 pitches -- all fastballs -- and recorded three groundball outs.
"Once I got that first strike, I felt like I was back in it," said Luebke, who made it to Petco Park for the conclusion of Saturday's game. "I got that one out of the way, then I was just trying to get outs."
Luebke went to the bullpen after his inning and threw about 15 more pitches, he said, incorporating his offspeed and breaking stuff. He is slated to make another appearance Tuesday.
• The Padres acquired 23-year-old left-hander Brad Wieck from the Mets on Saturday, completing the trade that sent Alex Torres to New York. Wieck, a seventh-round pick of the Mets in 2014, had a 3.21 ERA for Class A Savannah with 74 strikeouts and 21 walks in 56 innings (10 starts).
Wieck will be assigned to Class A Fort Wayne. The Padres also acquired reliever Cory Mazzoni (currently with Triple-A El Paso) in that deal.
• Brandon Morrow, who suffered a setback last week in his recovery from right-shoulder inflammation, won't begin throwing again for 7-10 days, Padres manager Bud Black said. The right-hander felt shoulder discomfort in a rehab start for Double-A San Antonio on Sunday.
Morrow is 2-0 with a 2.73 ERA in five starts this season.
AJ Cassavell is a reporter for MLB.com. Follow him on Twitter @ajcassavell. This story was not subject to the approval of Major League Baseball or its clubs.