The radio and television host kept a low profile on the flight, and several passengers said they didn't recognise him.
Holmes had suffered from hypertrophic cardiomyopathy, in which the heart muscle thickens and impedes blood flow.
He was flown to Auckland after the usually genetic condition was confirmed by his Hastings cardiologist on May 30 and had a four-hour operation a week later.
He was placed in a coma to speed his recovery, and awoke last weekend.
Holmes previously told the Herald he was "a bit scared" about the operation but had confidence in Auckland City Hospital staff.
"This is a biggie, but I have every confidence in the team," he said. "We will get through."
Holmes had also been positive about his long-term prognosis, including a return to work as a Newstalk ZB and TVNZ host and Weekend Herald columnist.
A statement issued on behalf of Holmes and his wife, after he was placed in the coma, thanked the public for their support.