The model measures 23 feet across and is 500,000 times smaller than the moon itself. It is made up of thousands of Nasa satellite images of the moon's surface.
It features alongside Tim Peake's Soyuz TMA-19M space capsule.
The cathedral, which is celebrating its 900th anniversary this year, won a competion to become the sixth location to host the Soyuz space capsule as it makes a tour of eight cities across the UK.
It has been presenting a programme of space-themed activities during the exhibition, including a StarDome presented by Leicester's National Space Centre and now, the Museum of the Moon by Luke Jerram.
The Very Rev Chris Dalliston, Dean of Peterborough, said: "We are delighted that Museum of the Moon will join Tim Peake's Spacecraft in the Cathedral during our 900th anniversary year.
"Just as the Cathedral has been lifting our eyes heavenward for centuries, so these contemporary works of art and science help us to do the same, prompting questions about our place in the universe, and the mystery and love of God that lie at the heart of it."
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.