Ainge provided the update during an appearance on WBZ-FM's Toucher and Rich radio show.
Hayward suffered a gruesome injury to his lower left leg just over five minutes into his debut with the Celtics after he signed with the team as a free agent in July.
The 27-year-old Indianapolis native, who suffered a dislocated ankle and fractured tibia, underwent surgery on Oct. 18. The team announced there was no timetable for his return.
The Butler University product confirmed that outlook in a November Facebook post.
"Finally, the Celtics organization has been just over the top in every aspect," he wrote. "They know I will not be back on the court at all this season, but they have been making sure I have every resource I need, and are making me feel like I am a part of the team. The entire Celtics family is filled with so many incredibly caring people."
Despite losing Hayward on opening night, the Celtics currently own the NBA's best record at 22-4.
Along with the MVP-caliber play of point guard Kyrie Irving, young forwards Jaylen Brown and Jayson Tatum have also emerged to help Boston fill its void on the wing.