The mural, in the city’s St Stevenson Square, was spray-painted last month by street artist Akase in tribute to Mr Floyd, who died in the hands of Minneapolis police in May.
Council bosses said they were doing everything in their power to find out who committed the “abhorrent crime”.
Police are reviewing CCTV footage in a bid to identify the vandal who is thought to have struck some time between Tuesday night and the early hours of Wednesday.
The portrait has been boarded up until repair work gets underway.
Disgusting. A racist has defaced the George Floyd memorial in Stevenson Square. This is not how we act in Manchester. pic.twitter.com/bXYQ7Wtyvk— The Manc (@TheMancUK)July 22, 2020
Nigel Murphy, deputy leader of Manchester City Council, said: “It is utterly sickening that this type of behaviour exists in our society.
“We are currently reviewing CCTV footage in the area and we will do everything we can to find out who committed this abhorrent crime.
“Manchester is a place that celebrates our diversity and we will not tolerate hate in our city.
“In the short term we have chosen to cover the mural because it’s intolerable to see such language on our streets.
“It is possible to clean the graffiti from the wall, but this will most likely also remove part of the mural.
“Our preference is to work with the artist to paint over the offending graffiti and restore the mural of George Floyd as soon as possible.”
Greater Manchester Police said: “At around 8.20am on Wednesday, officers were on a routine patrol in the Northern Quarter area of Manchester city centre when they found racially aggravated criminal damage in Stevenson Square.
“An investigation is under way. No arrests have been made.”
Anyone with information is asked to contact police on 101 quoting 610 of 22/07/20.