The singer, 24, ended her show singing Rehab from the photo pit when the scuffle broke out.
It was not clear at the time what caused it, but festival boss Michael Eavis later told the NME the fan had grabbed Amy's breasts.
Other reports suggest the fan tried to touch her trademark beehive hairdo.
Police say they received no complaint of assault after the gig, and that no investigation has been launched.
Amy also performed at Nelson Mandela's 90th birthday concert in Hyde Park on Friday.