Officers had tried to speak to the driver of the white SUV after it was parked in the driveway of the consulate in the city's eastern suburbs on Monday morning.
Instead, the 39-year-old man behind the wheel drove the vehicle through the property's gates and onto its lawn, police allege.
Helicopter footage showed the vehicle with its doors flung open and smashed front windows parked by a large flagpole.
The man was taken to Surry Hills Police Station, where he is being questioned.
The car was towed from the consulate about 10am as federal police detectives investigated.
A 24-year-old constable sustained a hand injury and was treated by NSW Ambulance paramedics.
Pro-Kremlin influencer Simeon Boikov, who goes by the moniker Aussie Cossack online, has been holed up at the consulate for 1000 days after he was charged with assaulting a pro-Ukraine protester in Sydney.
He was woken by the sound of police sirens about 8.30am and, after initially thinking there was a fire next door, emerged to find the Toyota parked on the consulate's lawn.
Boikov said the driver was already being pursued by police as he drove through the compound's gates.
"From my side, it looks like a diplomatic asylum attempt," he told AAP.
Boris Kragen, 77, a Russian national from Moscow, was surprised when he saw the leafy street taped off and several police cars blocking the area around the consulate.
"I came here to do some paperwork but they (police) said it's closed, so now we wait," he told AAP.
Minor damage to the front gate was quickly repaired.
The area was being guarded by federal police officers.
AAP has contacted the Russian consulate for comment.
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