The fire started just after 1.20pm on Sunday in a skip at the Fengate centre.
The site had to be closed for the rest of Sunday and all of Monday as works to clear the site after the fire - and an investigation - were carried out.
A spokesman for Cambridgeshire Fire and Rescue Service said the fire was started accidentally - and a Peterborough City Council spokesperson said no one was injured in the incident.
Today the council spokesperson confirmed the centre would re-open as normal today.