The 32-year-old Canberra suspect appeared in the ACT Magistrates Court on Tuesday to face five charges, including failure to stop for police and driving while suspended, the Australian Broadcasting Corporation (ABC) said, citing court documents.
He was denied bail.
An ACT policing statement on Monday said police had received a report that a man had threatened a woman with a firearm and allegedly stolen a car.
The statement said police formed a cordon to intercept the man.
He was arrested in Canberra and the vehicle was recovered about 9:05 a.m. on Monday, about half an hour after the alleged offence began.
The ABC said the man had pointed a long-barrelled gun at Kyrgios's mother Norlaila and demanded the keys to a green Tesla.
Kyrgios helped police track down the car by using a location app on his phone, the ABC added, citing court documents.