The Lord of the Rings director had been suffering from acute stomach pains, which later turned out to be a perforated ulcer. He was admitted to a Wellington, New Zealand hospital last Wednesday.
A representative for the hospital said that Jackson is "doing well" following the surgery.
The filmmaker is expected to remain at the facility for a few more days.
The procedure delayed the start of shooting on two-parter The Hobbit, which is scheduled for release in December 2012 and December 2013.