The Ephraim Palace in the former eastern half of the capital was renovated in 1987 - the dying days of the socialist regime.
To commemorate the rebuilding, in the historic Nikolai quarter by the Spree, a plaque was placed on a wall of the foyer noting the re-opening of the building "in the presence of Comrade Honecker."
Honeker, who died in exile in Chile aged 81 after the collapse of his regime, was widely despised by East Germans before the fall of the Wall - so much so he finally gave up power to a successor, Egon Krenz, in a failed bid to shore up the government's popularity just three weeks before the end.
Now Christian Democrat councillor Florian Schwanhäuser is demanding the memorial be taken down, saying that it insults the victims of the dictatorship that ran East Germany.
"This plaque must go!" he told Bild newspaper, echoing the rallying call of former US President Ronald Reagan, who stood in front of the Brandenburg Gate in 1987 and demanded of USSR leader Mikhail Gorbachev "Tear down this wall!".
"It is in appropriate to find Honecker cited in this way."
The museum is owned by the city government, and Schwanhäuser has formally demanded to know why it hasn't already been removed.
But Green party councillor Sabine Weißler insisted "This plaque is treated as a historical document. We intend to let it stay hanging there."
In fact, the whole building is under historical protection.
The Ephraim Palace was originally built in the 18th by the court jeweller to King Freidrich II, and its rococo facade and prominent location on the junction of two streets led it to become known as the "most beautiful corner" of Berlin.
The building was partially dismantled in 1935, although its facade was carefully restored and rebuilt in 1987 as part of Honecker's grand plans for the 250th anniversary of Berlin.
But the head of the Stasi Museum in Berlin, housed in the former HQ of the feared secret police, told the newspaper the plaque should go.
"This plaque should be completely replaced and sent to the German Historical Museum," Hubertus Knabe said.
"It cannot be that in the name of historical protection we pay homage to a dictatorship."
Whilst the plaque will stay put for the time being, the CDU have said that at the very least a second one should be erected explaining why Honecker's name appears on the original plaque.