An unlicensed driver accused of running down a Brisbane police officer who tried to pull him over for speeding will remain behind bars.

Jordan James Rogers allegedly fled after hitting the senior constable at Tarragindi on Sunday afternoon, leaving the 57-year-old with leg and hip injuries.

The officer remains in the Princess Alexandra Hospital in a stable condition.

Rogers, 24, was later found at Salisbury and charged with offences including dangerous operation of a motor vehicle, serious assault of a police officer causing bodily harm, and failing to remain at a road incident.

He didn't appear when his matter was mentioned in the Brisbane Magistrates Court on Monday and there was no application for bail.

Rogers will remain behind bars and appear at Holland Park Magistrates Court on April 16.