The rock hero told BBC radio he fractured the little finger of his left hand when he tripped over a stone slab in his garden.
The accident caused the hard-rocking British band's concert at London's O2 Arena to be put back from November 26 to December 10. The legendary group split in 1980 and have not played together for 19 years.
"I didn't just come down on my hand, I came down on other parts of my body as well. But of course it was the hand that had a bit of an injury to it," said Page, 63.
"It's got a fracture in the little finger of the left hand, which is a nuisance because it's really needed. It's just going to take a little while for it to heal, that's all.
"It's not permanent damage. I've broken fingers before, a lot worse than this."
The guitarist said he expected to resume rehearsals soon.
"We'll make the gig all right and we'll do all the rehearsals too. It's just going to need like two, two and a half weeks," he said.
Fans could expect to hear the band's classic songs at the gig, Page added.
"It's pretty much a lot of the songs that people would want to hear. We just got together and started playing and it started to take on its own shape, if you like," he said.
"It's probably what you'd want to hear, and what we want to play too, so that's a great, great chemistry."
Singer Robert Plant wants to do "one last, great show" and has insisted it will not be followed by a tour.
Led Zeppelin split in 1980 following the death of drummer John Bonham, who choked on his own vomit following a drinking binge.
More than one million people applied for the 20,000 tickets after the reunion gig was announced.
The concert is a tribute to Ahmet Ertegun, the late founder of the Atlantic Records label, who signed the group in 1968.
Plant, Page and bassist John Paul Jones, with Bonham's son Jason on drums, will headline the gig.
Led Zeppelin has sold more than 300 million albums worldwide and the group was inducted into the Rock and Roll Hall of Fame in 1995.

Copyright AFP (Agence France-Presse), 2007