Burgess sustained a fractured cheekbone in the opening seconds of the showpiece on Sunday, but carried on and put in an inspirational performance as South Sydney Rabbitohs defeated Canterbury Bulldogs 30-6.
The Englishman was visibly emotional in the closing stages of the game, and will now depart Australia to switch codes and join Premiership outfit Bath.
However, the procedure to fix the problem has cast doubt over the date for Burgess' arrival at his new club.
"He'll come out of hospital and the surgeons will have to sit round a table with the South Sydney doctor, and then communicate to our medical team when he can fly over and how long he'll be out for," Bath head coach Mike Ford told BBC Points West.
"I knew he wouldn't come off because he's a tough guy. But I knew he'd done something serious as he got up from that first tackle and pointed to his cheekbone.
"It's a blessing in a way, I think. We were always going to give him time off when he came over. We've now got the comfort that we can't play him anyway.
"We were only ever going to play him when he was ready. We weren't going to push him out there when he doesn't know the laws of the game."
Burgess had been due to arrive at Bath on October 15.