Church and Anderson crashed into each other in shallow right field while chasing Andruw Jones' fourth-inning popup during New York's 1-0 victory over the Los Angeles Dodgers, the latest injuries for the Mets this spring.
First baseman Carlos Delgado is feeling discomfort in his right hip and returned to New York for an MRI, which was negative.
A woozy Church, the team's new right fielder, was helped off the field and won't play again until he is free of concussion symptoms, the Mets said.
Anderson, a pinch-hitting specialist who was playing first base, walked off under his own power. He has a bruised sternum and is day to day.
"I don't think it's anything serious," Anderson said.
Both players had CT scans that came back negative.
The play brought back memories of a gruesome 2005 collision between Mets outfielders Carlos Beltran and Mike Cameron, who banged heads at high speed while pursuing a drive to right-center in San Diego.
Cameron, now with Milwaukee, was seriously injured on that play. This time, Church took the brunt of the blow as he tried to make a basket catch on Jones' blooper. The ball popped out of Church's glove and fell for a single when he and Anderson collided.
"It's always a little scary when you see stuff like that," Mets manager Willie Randolph said. "It's hold-your-breath for a second, but I think Marlon might be OK. We'll see how he feels tomorrow morning, but I think Ryan's going to be out a couple days. We'll see how he feels."
Randolph said Church didn't lose consciousness.
"He was OK. He was just stunned," the manager said.
The Mets already are struggling with injuries. Beltran, Damion Easley, Endy Chavez, Luis Castillo and Ben Johnson are among the position players who haven't played in a Grapefruit League game yet due to aches and pains.
Delgado has an impingement in his right hip and is expected to sit out for a couple of days. He was returning to Port St. Lucie on Saturday night.
"He's very important for us," Randolph said. "He's a big part of our offense and he needs to obviously bounce back from an off year."
All-Star shortstop Jose Reyes also fouled a first-inning pitch off his shin and hobbled around the batter's box before returning to finish the at-bat. He remained in the game.
"If we get all of the kinks out of the way early, get them out of the way now. I mean, golly," Randolph said.
Dodgers ace Brad Penny threw 38 pitches in two scoreless innings, allowing one hit and a walk while striking out two.
"He's not where he's going to be later in the spring, but I thought he threw the ball pretty good," Dodgers manager Joe Torre said. "I thought he turned it up a bit when he had men on base."
Penny did not address the media after the outing because he jumped in a limousine and headed to the airport. He was set to meet his father for a flight to Ohio to watch a friend compete in an Ultimate Fighting Championship bout.
Chan Ho Park followed Penny with two scoreless innings.
Mets prospect Jonathan Niese started and tossed two shutout innings with three strikeouts.
"The confidence is great," Niese said. "The more I work, the more confident I get."
The teams combined for only six hits. New York won when Brady Clark was hit by Rick Asadoorian's pitch with the bases loaded in the bottom of the ninth inning.