The party says Willie Young, the Labour finance convener at the city council, has turned Aberdeen into a laughing stock.
The call follows a long-running battle between Labour and the SNP stretching back to Mr Salmond's visit to a local primary school during a by-election campaign.
It escalated when the First Minister sharply criticised Mr Young for his handling of a decision which he says could cost the city more than £7 million in funds.
The row came to a head this week when Mr Young said the council will ban the SNP leader and all his ministers from carrying out any official business on council property, including parks.
Relations hit a "new low", Mr Young noted.
His unusual call was swiftly watered down at a full council meeting today where members were asked instead to revise the protocol of ministerial visits.
The SNP tried to pass a motion of no confidence but were ruled out of order.
Callum McCaig, the SNP group leader on the council, said: "Councillor Young's actions were an affront to democracy. He has brought this city into disrepute and his position as finance convenor is utterly untenable.
"Ruling against a motion of no confidence seeks only to insulate councillor Young from a growing public clamour for him to be removed from office."