The assault happened during England's match against Uruguay in Sao Paulo on June 19.
England lost the Uruguay match 2-1 after two goals from Luis Suarez, who found himself in trouble with football's world governing body FIFA for biting an Italian player in a later match.
The result effectively ended England's chances of qualifying from the group stage of the World Cup and their early departure from Brazil was confirmed when Costa Rica beat Italy the following day.
Confirmation of the incident came after radio pundit Stan Collymore tweeted he had seen footage of a "fan attacked", the BBC reported.
Six police British police officers have travelled to Brazil for the tournament to offer support and advice to Brazilian police and local authorities as well as overseeing the thousands of England fans who travelled to the country.
The Association of Chief Police Officers issued a statement following former Liverpool and Nottingham Forest striker Collymore's tweet.
Chief Superintendent Rachel Barber said her officers were made aware during the match "that an incident had taken place which resulted in an England fan having a portion of his ear bitten off by another England fan".
"During the course of our pursuit of the assailant, we located and interviewed several witnesses. They were very helpful in giving their version of events, but, unfortunately they were unable to give us a name for the alleged attacker."
She said officers observed supporters at England's final match against Costa Rica on June 24 in Belo Horizonte "but it appears he did not travel to that game".
A Foreign Office spokesman in London said: "We are aware of an incident in Sao Paulo on June 19 involving a British national and we provided consular assistance.
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