The Red Cross ambulance crew had answered a call in Freiburg, southern Germany, and in their hurry, parked their vehicle in the street outside the family's house, according to a report in Der Spiegel.
They left the blue lights flashing and the heating on, in case they had to take the child to hospital – and therefore had to leave the keys in the ignition.
But having sorted out the emergency and successfully treated the child, the team left the house to find no trace of their ambulance.
“Whoever does this kind of thing is putting people's lives at risk,” said Wolfgang Schäfer-Mai, manager of the Red Cross in Freiburg.
“What would have happened if the crew had needed further equipment from the ambulance I order to save the life of the child? What if the child had to be taken straight to hospital?”
The central office used a GPS tracing system to find the ambulance which had been dumped just a few streets away.
Police have reportedly arrested a 41-year-old man in connection with the theft.