Jackson was admitted to a hospital in Wellington, New Zealand on Wednesday suffering from acute stomach pains, which later turned out to be a perforated ulcer.
Shooting on the highly-anticipated J.R.R. Tolkien adaptation was due to begin in mid-February, but a spokesperson for Jackson has now confirmed that the start date has been pushed back while the 49-year-old recovers from the operation.
Publicist Melissa Booth said in a statement: "Sir Peter is currently resting comfortably and his doctors expect him to make a full recovery.
"The surgery is not expected to impact on his directing commitment to The Hobbit beyond a slight delay to the start of filming."
The Hobbit two-parter is currently scheduled for release in December 2012 and December 2013.