The ambulance driver had stopped to use an ATM on Friday afternoon, said Sergeant Noloyiso Rwexana.
While he was busy, the man opened the door, stole the cellphone and ran off.
The driver was able to give a good description of the man to public safety and armed response officers, according to the Somerset West Neighbourhood Watch Facebook page.
They spotted the man and questioned him with the help of an off-duty police officer from Macassar police station.
The man had apparently already sold the phone.
Rwexana said they arrested the 21-year-old on a charge of theft out of a motor vehicle.
He would appear in the Somerset West Magistrate's Court on Monday.