The defenseman was placed on injured reserve retroactive to March 2. He has missed three games because of the illness.
Heiskanen scored 29 points (four goals, 25 assists) in 52 games and led Dallas with an average ice time of 24:46 per game.
Dallas is 2-1-0 without Heiskanen, with Joel Hanley replacing him. The Stars will have to rely more on defensemen Ryan Suter, John Klingberg, Jani Hakanpää and Esa Lindell, who have averaged more than 24:00 in their past three games, a significant increase in playing time for each of them.
Hakanpaa's ice time has gone up the most, to 26:27, after he averaged 15:17 in his first 52 games. He played what had been his NHL-high 25:14 in a 4-3 overtime win at the Winnipeg Jets last Friday, topped that with 28:35 in a 6-3 win at the Minnesota Wild on Sunday, and then played 25:32 in a 2-1 loss at the Nashville Predators on Tuesday.
"That's a lot of minutes," Stars coach Rick Bowness said Tuesday. "He plays his heart out every shift. Jani is the least of our worries because he gives you everything he has every shift. He needs a little help sometimes from the other guys on the ice, but he gives you everything he has.
"When Miro comes back it'll take some minutes away for sure, and we'll break the puck out a lot better when Miro comes back as well. He's not there and you adjust, but 'Hak' is the least of our worries."
Suter has led the Stars the past three games, averaging 27:12, about four minutes more per game than he was playing (23:16). Klingberg has averaged 25:16 in his past three games, up from 21:49, and Lindell is up nearly two minutes, to 24:14 from 22:16.
Thomas Harley and Hanley have combined to average 18:13 per game.
The Stars have been one of the hottest teams in the NHL, 14-5-1 since Jan. 20. Their .725 points percentage during that time is fifth.