An RSS worker was shot at in Garden Reach area of south-west Kolkata on Monday, police said, adding that they were yet to identify those behind the incident.
The BJP alleged that the attack was a handiwork of Trinamool Congress men and police is trying to protect the culprits.
Bir Bahadur Singh was shot at by two men who came on bike around 10 am. He was then rushed to a hospital where he is undergoing treatment, police said.
"We are investigating the case," a police official said.
Singh is said to be a well-known RSS functionary in the area.
The TMC, however, has denied any involvement in the attack.
The BJP demanded immediate arrest of the culprits.
"In West Bengal, the Hindus and Hindutva organisations are at risk and breathe everyday at the mercy of God. So we pray to God for the speedy recovery of Bir Bahadur Singh who was shot at," West Bengal BJP president Dilip Ghosh said.