The boy rolled under the rear wheels of the fiaker, which crushed his chest and lungs.
Police said that the boy was able to open the door of the carriage, unobserved by his family, and fell out. “He leaned against the door, fell into the street and was run over by the left rear wheel of the coach, in his chest area,” police spokesman Paul Eidenberger told Radio Vienna.
The boy suffered serious injuries to his chest and lungs and was taken to hospital. He is in a medically-induced coma and is on a ventilator. Doctors say he is currently stable but that his condition could change at any time.
The accident happened early on Saturday evening in Strauchgasse in Vienna's first district.
The boy was in the carriage with his parents and his brother. The fiaker driver said that he had not noticed that the boy had fallen out as he has been concentrating on the traffic. It was only when he heard the parents screaming at him to stop that he realised something was wrong.
Eidenberger said that the family come from the Czech Republic and are in Vienna for a holiday. He added that both the fiaker driver and the boy's mother are being investigated “as a matter of routine”, on suspicion of negligence and causing bodily injury. He did not give any further details.