Council citifleet team leader Brent Bachop said the piece of playground equipment had been installed in a leased space in the council's Crawford St car park at the weekend.
It was discovered on Monday morning and quickly brought to the council's attention, he said.
Whether the seesaw's appearance was supposed to be a message directed at the council or the occupier of the leased space was not clear.
Whoever was responsible had cut small holes into the asphalt and cemented the legs in place before departing, leaving staff - and the user of the leased space it occupied - to ponder the meaning, Mr Bachop said.
"I have never had it before, that's for sure.
"It's definitely not the ordinary - graffiti is about the worst we normally get," he said.
It is not the first time the council's parking infrastructure has been targeted.
In September, sacks were placed over parking machines and lights across the city centre in protest at the council, with one reading "The machines work, the council is out of order".
A member of the group linked to the appearance of the sacks, Moray Pl gallery owner David McLeod, said yesterday he knew nothing about the seesaw's installation "and that's scout's honour".
However, he thought the work could symbolise the council's "flip-flopping" on issues.
Mr Bachop said contractors planned to remove the seesaw and patch up the car park's holes yesterday.
Figuring out the message behind the stunt might take longer, however.
"I have no idea - you know as much as me."
