Martinez was the Tigers' starting catcher on Friday for the first time since Aug. 4, 2011, before he suffered a knee injury and missed all of last season recovering from surgery to repair a torn anterior cruciate ligament.
On Sunday, he was back behind the plate again. Leyland said he doesn't want it to become too big of a deal.
Martinez was clearly excited to catch again before Friday's game. Torii Hunter joked about how Martinez was trying on all of his catching gear on Thursday in anticipation of returning to his old position.
While Martinez called a good game working with Doug Fister on Friday, he said he didn't feel the need to prove he can still catch.
"I don't think I have to show anything to anybody," Martinez said. "First of all, I know my role. Since I got here, I knew I was going to be mainly a DH, catching once in a while when Alex [Avila] gets an off-day. Unfortunately I had a bad injury, missed the whole year."
Leyland said he understands Martinez's excitement to get behind the plate again, but knows he's not an everyday catcher anymore.
"He's fired up. He likes to play. He's getting smarter," Leyland said. "Normally, he'd say he could still catch every day. He can't. He's figured that out. He can't do it every day on an everyday basis. Victor's really a bright guy. He loves to compete."
Chris Iseman is an associate reporter for MLB.com.