The convoy of Singh, elected from Kathua-Doda-Udhampur Lok Sabha seat, was on way to Banihal in Ramban district when the accident happened, police said.
The lawmaker was travelling in the Ambassador car when a tyre of the vehicle burst in Mand area in Tikri belt, they said.
"It was a narrow escape. The wheel along with the shaft came out and the vehicle slided for over half-a-km," the MP told PTI.
Singh was later shifted to another vehicle, police said adding the MP was to take part in a function in Ramban.
"I had raised the issue of this old vehicle with Chief Minister Omar Abdullah and police in the past and has asked for its replacement", Singh said adding nothing was done.
"The bullet-proof vehicle had come back to us just a day before our visit to remote Banihal constituency," he said.