The incident happened when President Mukherjee was going to Kanidighi, about 25 kilometers from the MDI helipad in Murshidabad, to inaugurate a school, officials said.
After some time, officials in the tail car, the last car in the 20-vehicle cavalcade, heard the siren of an ambulance.
Wasting no time, the presidential motorcade gave way so the ambulance could pass through, they said.
It was not immediately clear who was inside the ambulance.
President Mukherjee began a two-day tour of West Bengal, his last visit to his home state as president.