TV and radio presenter Glenn Wheeler is in an induced coma after being knocked off his scooter and seriously injured in Sydney's south.

Mr Wheeler, who appears on Network Seven's The Morning Show, was riding his scooter when he was involved in a crash with a wagon at Woolooware on Saturday afternoon.

The 54-year-old suffered serious head injuries and severed an artery in one leg.

Mr Wheeler, who also presents for 2GB radio, had some bleeding on the brain but scans came back with encouraging results.

"He's in an induced coma and his condition is stable," his family said in a statement.

"We're thankful to emergency services, members of the public who offered assistance and the wonderful staff at St George Hospital."

The driver of the other car involved in the crash was arrested on Saturday and underwent mandatory blood and urine tests.

A woman was charged with negligent driving occasioning grievous bodily harm and another traffic offence.

The 59-year-old was granted bail in Parramatta Court on Sunday.

The case was adjourned to Sutherland Local Court on February 19.