Letang was previously out of action for two months after suffering a stroke in 2014, with subsequent tests showing he was born with a small hole in the wall of his heart.
Speaking to the team's website, Pittsburgh's general manager Ron Hextall revealed the 35-year-old had suffered symptoms on Monday before undergoing testing, which will continue in the coming days.
"Kris reported symptoms to the training staff on Monday and was immediately taken to the hospital for testing," Hextall said.
"The test results were shocking to hear, but we are grateful that Kris is doing well. We are thankful to the medical staff and the physicians at the University of Pittsburgh Medical Center.
"He is a warrior on the ice, but first and foremost, he is a son, father, husband and friend. His health is our number one priority."
Letang, meanwhile, is optimistic he will make a swift return to action.
"I am fortunate to know my body well enough to recognise when something isn't right," Letang added. "While it is difficult to navigate this issue publicly, I am hopeful it can raise awareness.
"It is important for me that my team-mates, family and the fans know that I am okay. I am optimistic that I will be back on the ice soon."
Letang has spent the entirety of his 17-year career with the Penguins, playing 962 regular-season games, 543 of which have come since he suffered his first stroke eight years ago.