The incident happened at the junction of Holburn Street and Holburn Road at about 03:00.
Police Scotland said officers briefly gave chase when the vehicle failed to stop for them in Crown Street, but they gave up their pursuit for safety reasons.
The car then hit an office building.
Insp Megan Heathershaw said: "Thankfully, no one appears to have been injured during the incident, however some damage was caused to a building in the Holburn Street area.
"I would like to take this opportunity to stress that during incidents of this nature, vehicles will only be followed when safe to do so. The safety of the public throughout remains at the forefront of our priorities.
"Inquiries are ongoing and I would urge anyone with information to contact police."

A firmer dollar in the aftermath of the first Clinton-Trump presidential debate helped send gold prices lower.
The Dow Jones Average was up 0.74% to 18,174, while the more tech-related Nasdaq rose 0.92% to 5,284. The broader S&P 500 index gained 0.64%.
Stronger consumer confidence data helped to boost retail stocks.
High street firms Macy's and Best Buy gained 1% and 2% respectively.
Technology shares were strong, with Facebook and Google parent Alphabet both rising 1.1%, and Amazon adding 2.1%.
Oil-related shares retreated on lower crude prices, with Anadarko Petroleum losing 0.5% and Halliburton down 1%.

The 25-year-old man reportedly calls himself Harald Hitler.
The man, sporting a side parting and a trademark moustache, had been seen having his photograph taken outside the house in Braunau am Inn in which Adolf Hitler was born.
The lookalike had recently moved to the town on the German border, police spokesman David Furtner told the BBC.
Mr Furtner said this was not a joke or a piece of performance art.
"The young man knows exactly what he is doing," the police spokesman said.
He said the man had also been spotted in Vienna and Graz.
Pictures of the man were published by Austria's Heute.at news website on Monday.
Glorifying the Nazi era is a crime in Austria.
Last October, the Austrian authorities decided to demolish Hitler's birthplace house to stop it becoming a focal point for neo-Nazis.
Hitler was born in a rented room on the top floor of the building on 20 April 1889.
During Nazi rule, the house was transformed into a shrine to Hitler as the town drew in a wave of tourists.
But as the Nazis began to lose control in 1944, it was shut.
A man was taken into custody after a truck which had been involved in a police pursuit crashed into a building in Aberdeen.
[NEXT_CONCEPT]
(Close): US markets closed higher, led by technology and consumer sectors, while oil prices fell on fading hopes of an Opec deal to limit output.
[NEXT_CONCEPT]
A Hitler lookalike has been arrested in Austria on charges of glorifying the Nazi era, local officials say.