Marcum headed to New York for a cortisone shot in his right shoulder while the Mets were beating the Houston Astros 7-5 Wednesday.
Manager Terry Collins expects the right-hander to return for another spring training start early next week.
"He said he gets it every spring, pretty much," Collins said. "He just wanted to get it cleared up early so he can take a couple extra days now and he can go into his last start of the spring and extend himself a little bit."
Marcum, a winter free-agent singing, isn't the first Mets starter to have health issues this spring. Johan Santana hasn't pitched in a game as he builds strength in his throwing shoulder.
Also, Closer Frank Francisco has been sidelined because he is bothered by the same elbow inflammation that ended his 2012 season on Sept. 16 and Reliever Pedro Feliciano is dealing with a heart issue.
Matt den Dekker broke a tie with a two-run triple in the seventh inning and the Mets came back from a five-run deficit.
"I feel real good about where I'm at," said White, a sinkerball pitcher acquired in a winter trade from Colorado. "I've still got to pitch, still got to get guys out. We've got a week and a half of competition left."
"Spring for me is always about getting ready," said White, who went 2-9 for the Rockies last season after starting the season in Triple-A. "This year is a little different because I knew I was competing for a spot, and I came in a lot fresher. I feel good and I feel like I'm ready for the season."
Peacock was scheduled to follow White on Wednesday night, but manager Bo Porter moved him back to Thursday after getting a report of threatening weather.
"You don't want to get a guy up to throw 10 or 15 pitches and then he's done, and this is a big outing for him," Porter said. "Tonight just wasn't the night to do it, not knowing what the weather was going to do."
Peacock will follow Harrell in Thursday's game against the Detroit Tigers.
Collin Cowgill's two-run home run off White started the Mets' comeback in the third inning.
Gee gave up five runs on seven hits in four innings, finishing his fourth start with three straight strikeouts.
Mets pitching coach" Dan (Warthen) got on him about making better pitches and he did a much better job in the last inning," Collins said.
Jeremy Hefner will replace Marcum as the starting pitcher for Thursday's game against the St. Louis Cardinals. ... Gonzalez, who has yet to start a game this spring, will pitch in an Astros minor league game Thursday.