The condition was discovered Thursday after Fleischmann experienced shortness of breath following the morning skate.
Team physician Dr. David Mellman said the 26-year-old Fleischmann will be on blood thinners for several months and will be held out of action.
"At the end of the day, fortunately this was discovered," Avalanche general manager Greg Sherman said before his team's 5-1 loss to Nashville on Thursday night. "He's a young man. This is a serious condition."
Sherman added that Fleischmann isn't in the hospital, and he should be able to resume his career following treatment.
"The indications from our doctor is yeah, he'll live a quote-unquote normal life," Sherman said. "This is something that can be treated through medication. That's what I'm told."
Fleischmann wasn't feeling well and reported his condition to head trainer Matthew Sokolowski, who sent him to see Mellman.
"He took it from there to do the necessary tests," Sherman said.
Fleischmann was acquired from Washington on Nov. 30 for defenseman Scott Hannan. The Czech had been a steady scoring threat since his arrival, compiling 21 points in 22 games. He also had his first career hat trick last month in Chicago.
"You just pray he's going to get healthy," teammate Paul Stastny said. "This is something you don't want to rush."
The illness to Fleischmann was the latest setback in an injury-riddled season for the Avalanche. The team has had quite a few of its top players miss time with ailments.
"We've dealt with adversity before," Sherman said. "I think the depth of our organization has come through in the past and I expect it to come through in the future."
As for who might take Fleischmann's place in the lineup, Sherman said he would speak to coach Joe Sacco on Friday morning. The team recently sent forward T.J. Galiardi to Lake Erie of the American Hockey League to help bolster his confidence.
Galiardi has struggled since coming back from a broken right wrist that sidelined him for more than a month. He's scored no goals in his past eight games.
"Tomas was a big piece for our team. But it's not the first time we've had to deal with injuries with our players," Sherman said. "It's the challenge of our business. We're not the only team that has to deal with it."
The Avs came out flat against the Predators, allowing two early goals. Avs coach Joe Sacco didn't necessarily think it had to do with an emotional letdown following the news of Fleischmann, just insufficient execution.
"We're all professionals. As much as you don't like to hear any news like that about any player, especially one of your teammates, you have to move forward. You have to carry on," Sacco said. "We've been very good at that."
Still, this hit the Avs hard.
"Obviously, it's a big [blow]," said Matt Duchene, who's on the same line as Fleischmann. "He has been one of our best forwards.
"It's tough to lose a guy like that, but we've been a team all year that's pressed forward when we've had injuries. So we're going to move forward, and hopefully he has a speedy recovery and gets back as soon as possible."