The ice cream based drink was laced with chocolate sauce and came with a small green army man, carrying a rifle.
Adventure Bar in Covent Garden was criticised after a Belfast man living in London checked out the menu and complained on social media about the name.
Adam McGibbon commented on the bar's Facebook account that the cocktail's name is "incredibly offensive" and "seems to almost mock the deaths of innocent people".
Thirteen people died in Londonderry when soldiers opened fire during a civil rights march on 30 January 1972. A fourteenth person later died from his injuries.
A 12-year public inquiry into what happened that day found the civilians were innocent and unarmed.
At the time Adventure Bar said the drink was "a tribute to the memory of those lost", adding that Bloody Sunday was a "dark day for all concerned".
They said those who were offended had taken the name out of context.
On Friday the bar posted on its social media page that they have removed the drink from sale.
"Adventure would like to again apologise unreservedly to everyone offended by the cocktail 'Sundae Bloody Sundae'," a statement said.
"It was never our intention to offend anyone and we removed the drink from sale permanently on Tuesday."