The occupants of the car allegedly ran from the scene after crash occurred at the intersection of Kianawah and Youngs Roads in Wynnum West about 9.20am.
Meanwhile, the 59-year-old motorcyclist had to be rushed to the Princess Alexandra Hospital in a critical condition.
The allegedly stolen car drove into the motorcyclist, according to police.
A 15-year-old girl and 15-year-old boy were arrested near the scene shortly after the crash.
They are currently assisting police with inquiries.
The car involved in the crash was allegedly stolen from a home in Wynnum West in the early hours of this morning.
Police are appealing for anyone with further information or dashcam vision of the vehicle, a white 2014 Nissan X-Trail with Qld registration 433VMK, to come forward.