The 1933 and 1934 teams won the Allan Cup senior men's Canadian championship.

In 1987, the Winnipeg Jets signed an agreement with the local ownership group in Moncton to provide players for the Moncton AHL franchise after the Calgary Flames and Boston Bruins folded the Golden Flames, purchasing the long-dormant Boston Braves franchise from the Bruins for the purpose.

Seeking to cut costs in a time when the AHL was beginning to withdraw from Atlantic Canada, the Jets folded the Hawks after the 1994 season, and joined with the Hartford Whalers in a dual affiliation with the expansion Springfield Falcons the following year.

The team featured several players who went on to have successful NHL careers including Kris Draper, Darryl Shannon, Stu Barnes and Dan Bylsma, who went on to win the Stanley Cup as head coach of the Pittsburgh Penguins.

In 1995, the Moncton Alpines of the QMJHL filled the void in the market that was left after the Hawks folded.