Police said the victim is a 27-year-old, who suffered head injuries, according to the Independent.
Eyewitnesses said the attackers were a group of three men, who shouted Islamophobic slurs as they drove past the mosque on Cannon Street Road.
They were calling people who came for the Friday prayers "terrorists," witnesses added.
Some of the worshippers tried to pursue them, which prompted two of the men to attack them with what is thought to be a hammer. After the attack, they dove into a moving car and drove off.
London police have so far been unable to detain anyone.
The attack occurred the same day 49 Muslims were killed in a terrorist attack at two mosques in New Zealand.
Following the New Zealand attack, police officers in the UK stepped up patrols around mosques on Friday.
Officers were deployed to provide reassurance and advice on protective security as Muslims attended Friday prayers around the country.
"Whilst there is no intelligence linking these appalling events in Christchurch to the UK, additional uniform patrols will continue in London and nationally over the coming days, focusing on places of worship and specific communities," Neil Basu, the national policing lead for counter-terrorism, said.
"We are paying specific attention to Mosques, particularly Friday prayers.
"Many communities will be understandably concerned and local officers will be out and about providing reassurance and protective security advice to communities, places of worship and businesses."
Sajid Javid, the British Home Secretary, is also due to hold talks with anti-terrorism chiefs and security officials to discuss possible further measures to protect mosques in the UK.