Matz pitched six effective innings against the Los Angeles Dodgers on Monday.
He said the forearm might have been bothering him during the start but that adrenaline dulled the issue until after he departed.
"It was pretty sore," Matz said. "I was still able to throw, but it was enough concern for me to say something to the trainers and just kind of tell them what was going on. Before I see the doctors, they just want to play it safe."
Assistant GM John Ricco said Matz will remain with the team for the remainder of the Mets' three-city trip, then be examined by team doctors as soon as Monday in Manhattan.
Right-hander Logan Verrett is expected to take Matz's turn Saturday in Colorado unless he is needed in relief during the current series against the Dodgers.
There are no plans to consider a stint on the disabled list for Matz before next week's medical examination.
Still, Mets officials do not want to play a pitcher short this weekend in Colorado, so they will promote left-hander Sean Gilmartin. Gilmartin spent all of last season working in relief at the major league level as a Rule 5 pick and is currently 4-1 with a 2.48 ERA while working as a starter at Triple-A Las Vegas.
Infielder Wilmer Flores will be placed on the disabled list with a left hamstring injury.
Collins said the Mets are being particularly cautious with Matz because of a bad experience with handling him last season. Matz felt lat discomfort after his 2015 major league debut but was allowed to proceed with his next start at Dodger Stadium. That potentially worsened the issue, and Matz subsequently spent two months on the disabled list.
Matz suggested he is not concerned this time. He took Wednesday off from throwing but intends to resume on flat ground Thursday.
"They've got me on some anti-inflammatories," Matz said. "Sometimes through the season you go through some nagging stuff. Last year I tried to pitch through it and ended up missing two months. So it's better to play it safe and give it the rest when I need it."
Verrett has been exceptional as a spot starter. He twice tossed six scoreless innings while filling in for Jacob deGrom earlier this season. Last year, while taking a spot start for Matt Harvey at Coors Field, Verrett allowed one run on four hits and a walk in eight innings.
After allowing seven runs and recording only five outs in his season debut, Matz is 5-0 with a 1.09 ERA in his past five starts.
"As the player, I want to go out, and I want to pitch my next start, especially with the way I've been feeling out there and the way my stuff has been," Matz said. "But it's not worth it to risk it right now. I'm feeling really comfortable with the progress it's made just in one day and taking the anti-inflammatories."