Further testing also revealed that Letang, 26, has a small hole in the wall of his heart that may have contributed to the stroke.
The condition is treatable with blood thinners and is not believed to be career threatening, the team said.
Letang has had the small hole in the wall of his heart since he was born.
He last played Jan. 27.
Letang was cleared by the team to go on vacation with his family during the NHL's Olympic break.
Letang has 18 points in 34 games this season.
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Nashville Predators general manager David Poile underwent two successful surgical procedures in the nose and eye areas on Friday to repair a facial laceration suffered Thursday when he was hit by an errant puck during the Predators' morning skate, the team announced.
The injury will prevent him from traveling with Team USA to Sochi on Sunday as planned, but he may join the American Olympic team in Russia later.
Poile led the selection committee that chose the players for the U.S. Olympic team.
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The Predators reassigned forward Taylor Beck to the Milwaukee Admirals of the AHL. Beck has played seven games for the Predators this season. He has no points.
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Injuries to Tampa Bay Lightning forward Valtteri Filppula and Minnesota Wild captain Mikko Koivu will prevent both from playing for Finland in the Winter Games in Sochi.
Forwards Jarkko Immonen and Sakari Salminen, both of whom are playing for Torpedo Nizhny Novgorod in the KHL, will replace them on the Finnish team, according to Urheilusanomat, a Finnish media outlet.
Koivu has not been cleared to play following ankle surgery performed on Jan. 6, the Minneapolis Star Tribune reported.
Filppula left Thursday's game with what was later diagnosed as a non-displaced fractured ankle, according to the Tampa Tribune.
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Team Sweden announced that it put Washington Capitals forward Marcus Johansson in place of injured Vancouver Canucks captain Henrik Sedin for the Sochi Olympics.
Johansson has seven goals and 29 assists for the Capitals, who will also be represented on Sweden's team by center Nicklas Backstrom.
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The Buffalo Sabres placed recently-acquired left wing Linus Omark on waivers.
The Sabres also demoted two rookies, center Phil Varone and defenseman Chad Ruhwedel, to the Rochester Americans of the AHL.