Wishbone Brewery in Keighley, West Yorkshire, said the deity was chosen "in all innocence" and would not be used again following complaints by religious leaders.
Rajan Zed, president of the Universal Society of Hinduism, had earlier called on Wishbone Brewery to apologise.
He said Hindu gods should be "worshipped in temples" rather than "used in selling beer for mercantile greed".
"Inappropriate usage of Hindu deities or concepts or symbols for commercial or other agendas is not OK because it hurts the devotees," Mr Zed added.
"Symbols of any faith, larger or smaller, should not be mishandled."
Wishbone head brewer Adrian Chapman said the brewer also considered calling the drink 'Indian Summer' and were unaware of any cultural appropriation because another brewery had called its product 'Black Jesus'.
"We would never, ever want to upset any faith or anything like that in the naming of any of our beers," he added.
"We try to pick interesting one-word names for the most part that aren’t used by other brewers.
"Other brewers use the name of a deity in their beers so I obviously never thought anything bad about it."
It has come to our attention that the name 'Ganesh' may cause offence to some folk. Would calling a beer after any deity be a cause for offence? When our Pumpclip stock runs out this beer will be renamed, suggestions being taken. Thanks :) pic.twitter.com/wSqZkcDzTn— WishboneBrewery (@WishboneBrewery) August 25, 2018
Wishbone’s Ganesh beer was described as a wit-style lime-infused beer with flavours of coriander, grape and camomile.
The Ganesh beer, produced in collaboration with Manchester brewery Beer Nouveau, was part of a "very limited" run that was never bottled.
Wishbone Brewery said the beer will be renamed should it ever be brewed again.
Brewer Chapman added he would be happy to speak to Mr Zed to reassure him the name Ganesh was chosen without any offence intended.