Martinez, 54, had a minor cardiac catheterization Monday in Washington, D.C. There is no timetable for his return. The Nationals announced Martinez would miss the game Monday, before the team lost 4-2 to the St. Louis Cardinals.
Chip Hale managed the Nationals in Monday's loss.
"Speaking to [Martinez] Monday, it really reassured me that he's doing great," general manager Mike Rizzo told reporters. "He's a tough, strong guy. I think that looking at what transpired today, we're happy and optimistic and hoping that he'll be able to make a full recovery."
A cardiac catheterization is used to diagnose and treat cardiovascular conditions, according to the Mayo Clinic. A catheter is inserted into an artery or vein and treaded through blood vessels to your heart.
Rizzo said Martinez was upbeat after the procedure.
Martinez left the dugout during the Nationals' 7-0 win against the Atlanta Braves on Sunday in Washington, D.C. He told members of the coaching staff he had chest pains before leaving the game around the sixth inning.
"We just keep playing," Nationals star Ryan Zimmerman told reporters. "Obviously we all miss Davey and hope he's well. But the game goes on, no matter who is here or not here. Whether it's a manager or player or anyone, you have to go out and play the game. I'm sure he would say the same thing.
"Obviously, we wish the best for him and we are thinking about him. But you just go out and play the game."
The Nationals face the Cardinals in the second game of the series at 7:45 p.m. EDT Tuesday in St. Louis.