Hayward underwent surgery to repair a dislocated left ankle and a fractured tibia in Boston on Wednesday night, a procedure that Bartelstein labeled a success.
"We expect him to make a full recovery and return to his All-Star form," Bartelstein said.
Earlier Wednesday, Hayward taped a video message to Boston fans from his hospital bed, and it aired to thunderous applause before the Celtics' home opener on Wednesday night against the Milwaukee Bucks at TD Garden.
Marcus Smart, the longest-tenured Celtic on a team that returned just four players from last season, was scheduled to deliver an address before the game. Smart instead directed attention to the video board for Hayward's message.
Wearing a hospital gown, Hayward told fans he'll be "all right" and said it pained him not to be with his teammates in Boston.
"What's up, everybody? I just wanted to say thank you to everyone who has kept me in their thoughts and prayers," Hayward said. "I'm going to be all right. It's hurting me that I can't be there for the home opener; I want nothing more just to be with my teammates and walk out onto that floor tonight. I'll be supporting you guys from here. I wish you the best of luck. Kill it tonight."
Celtics coach Brad Stevens said before Wednesday's 108-100 loss that Hayward was "down" after the injury that occurred a little more than five minutes into his Boston debut.
"I was [at the hospital] for a minute last night and also again today for an hour or so. He's down," Stevens said. "Obviously, there's a physical pain to it, but I think it's also doubled by the emotional pain of, you know, he put a lot of effort into trying to start this, his career, out well in Boston.
"But this is a setback; we're expecting a full recovery. And we know there are going to be a lot of tough days ahead on that recovery but, at the same time, hopefully he'll improve day to day. But it's been tough. It's been tough for him."
Stevens noted how his players' thoughts are on Hayward.
"I think the biggest thing is they really care about Gordon," Stevens said. "He's made a big impact on them. He's an easy guy to play with. He's a guy you want to play with on both ends of the floor. So certainly you miss that -- and that camaraderie. But one of the tasks that we have now is to pick up steam for him, and guys that get opportunities that [they] may not have [had before Hayward's injury] or guys that get opportunities from a more minutes standpoint need to be ready to take advantage of those."
Stevens said the Celtics will begin looking at how best to fill Hayward's vacancy, including a potential roster addition.
"I think that we will probably look at the roster spot," Stevens said. "We are bringing [rookie] Jabari Bird back and using one of his [G-League] two-way days today. I think we will at least be actively looking for that roster spot, just because, obviously, the standpoint of the youth, but also because you lose one of your better shooters and more versatile players. A guy who can put the ball in the basket for you.
"We'll see how that works itself out. We haven't really gotten into it too much because we have our hands full tonight."
Hayward, who was a free agent, signed a four-year, $128 million contract with the Celtics on July 1. The subsequent acquisition of Kyrie Irving put Boston firmly in the hunt in the Eastern Conference. According to ESPN's Bobby Marks, the team will likely be given an $8.4 injury exception to search for replacements for Hayward.
If Hayward is out for the season, the Celtics can collect on insurance by getting back $275,000 per game for the 41 games missed.
In all, the Celtics will be able to recoup approximately $11 million of the $29.7 million the team owes Hayward this season.
ESPN's Chris Forsberg, Jackie MacMullan and Darren Rovell contributed to this report.