The forward could return to the lineup as early as Thursday against the Ottawa Senators (9 p.m. ET; RDS2, SNW, TSN5, NHL.TV).
The Flames became the first team from the Western Conference to clinch a berth in the 2019 Stanley Cup Playoffs on Sunday.
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"I'm getting excited," said Neal, who sustained the injury Feb. 14 against the Florida Panthers. "You never want to be hurt, but you use that time to be ready for playoffs. The season is just starting for us now. We did a great job all year to put ourselves in a position to make the playoffs. There's nothing better than playoff hockey and winning in the playoffs. That's what I want to do. That's why I'm here. I'm looking forward to it."
Neal, who signed a five-year, $28.75 million contract (average annual value $5.75 million) with the Flames on July 2, has advanced to the Stanley Cup Final in each of the past two seasons.
He played with the Nashville Predators in the 2017 Final, won by the Pittsburgh Penguins in six games, and with the Golden Knights in the 2018 Final, won by the Washington Capitals in five games.
"He's obviously a guy who has had real good success in the playoffs and success the past couple of years going to back-to-back Finals," Calgary forward Matthew Tkachuk said. "To have him in this stretch for us is critical. He knows what it takes to win in playoff games.
"We need that."
The Flames followed the Tampa Bay Lightning from the Eastern Conference as the first two teams to have secured a playoff berth when the Minnesota Wild lost 3-2 in overtime to the New York Islanders on Sunday.