Manager Brad Ausmus said Martinez experienced a racing heart after his final at-bat during Saturday's 6-3 victory over the Chicago White Sox. Ausmus said Martinez spent the night in a hospital and that his heartbeat was regulated.
Martinez was expected to be released and travel by car to Detroit, where doctors will try to determine the cause.
"You don't mess around with the heart," Ausmus said. "We're not talking about a sprained ankle or something minor like that. This is something you take very serious because it could be life-threatening. That's what we're going to do. I don't know what's going to happen going forward."
Martinez, 38, was taken to the hospital in June after suffering from a rapid heartbeat, dizziness and cold sweats. He went on the DL and missed two weeks before returning to regular playing time.
Martinez is hitting .255 this season with 10 home runs and 47 RBIs in 107 games. He is under contract through the 2018 season and has said he plans to retire next year.
"The first question that Vic should ask, not me but the doctors, is, 'Is this putting me at risk? Is there any really long-term risk?'" Ausmus said about Martinez's future. "That would be the first question I would ask. Depending on the answer, you have to make a decision."
In the corresponding move, the Tigers recalled JaCoby Jones from Triple-A Toledo. Detroit had optioned the outfielder to Toledo on Saturday.
Detroit will rotate players at designated hitter while Martinez is out, Ausmus said.
The Associated Press contributed to this report.