The 23-year-old spent his birthday having an operation to repair a chronic compartment syndrome on his right arm.
The surgery was carried out by MotoGP specialist Dr Xavier Mir.
Mir's list of MotoGP patients include Hector Barbera - whom he treated this year when the Spaniard broke his leg - and Dani Pedrosa, after he broke his right collarbone during the 2011 season.
Bradl will be permitted to leave the hospital before the weekend, and will be able to start his functional recovery within three weeks.
"After the arm pump problem I suffered in Japan this year at Motegi GP I had my first medical check with Dr Mir two weeks ago and together with the team we decided to make this surgery quickly," Bradl said.
"The operation turned out really well and Dr Mir told me my arm was better than he thought, so I am really pleased we took the decision and operated.
"It's weird to celebrate the birthday at the hospital but some of my technicians came to visit me and the medical staff have been very nice with me."
Bradl was named MotoGP Rookie of the Year for 2012, having finished eighth in the standings for the satellite LCR squad.
He recently signed a two-year deal to compete as a Honda factory supported rider with LCR until the end of 2014.
He stepped up to the premier class after beating Marc Marquez to the 2011 Moto2 title.