Officials say some people have carried out cremations on the terrace roofs of houses in the city.
Many Indians regard the Ganges as holy and use its bank for cremations.
Hindus believe that if a person is cremated in Varanasi, the deceased will achieve release from sufferings of the cycle of birth and death.
Two of the 80 ghats - a series of steps going down to the water - lining the Ganges in Varanasi specialise in the business of human cremation.
"As the ghats are not available for cremation, the roofs of havelis [old mansions] and other old houses along the ghats are being used for cremation, but with great difficulty," Uttar Pradesh government spokesman Shailendra Pandey told AFP news agency.
Utpal Upadhyay, a long-time city resident, said this was the "worst floods in the holy city since 1978".
"The Ganges has risen, the banks are inundated, and people are not able to cremate. People are praying in their homes and flooded streets," he told the BBC.
Cremations have been also affected in the Hindu holy city of Allahabad, also in Uttar Pradesh, where pyres were being lit in the nearby alleys, an official said.
Floods across large swathes of India have killed at least 40 people and displaced tens of thousands of people.
More than 100,000 people have left their homes in recent days in Uttar Pradesh and the neighbouring state of Bihar as rain-swollen rivers have burst their banks, reports say.
At least nine people have died in Uttar Pradesh and another 15 in Bihar as flood waters hit villages and cities, disaster management officials said.
Several people have also been killed in the central state of Madhya Pradesh in the last 24 hours, according to the Press Trust of India news agency.
Floods are common in India during the monsoon season between June and September.
But excessive rains this year have caused the Ganges and its tributaries to rise above the danger level in about 20 districts in Madhya Pradesh, Bihar and Uttar Pradesh.
Floods in India's holy city of Varanasi in the northern state of Uttar Pradesh have forced a halt to cremations along the banks of the river Ganges.