The Ducati rider was caught in a four-rider crash at the first corner of the race.
The American, world title winner in 2006, had a screw inserted into his fractured scaphoid bone during surgery in California.
"Everything went pretty smoothly," Hayden said. "The scaphoid is a slow-healing bone so you don't want to wait, only to find out in January that it's not healing correctly.
"I'm happy to get it fixed right so that I'll be ready to go when I need to be."
Hayden expects to be fit for the first day of 2012 testing at the Sepang circuit in Malaysia on January 31.