The workers were constructing a toilet at a school next to the temple in Faridpur’s Madhukhali Upazila
Rahman, a former army chief, was admitted to Zia Heart Foundation in Dinajpur with head injury after the accident on Saturday.
His wife Nazzin Mahbub was given first aid.
Dinajpur BNP Vice-President Khalekuzzaman Babu said a human hauler hit Rahman's car from behind at Doshmile on Rangpur-Dinajpur Highway around 4pm.
Rahman was on his way from his in-law's house in Thakurgaon to Syedpur Airport to catch a flight to Dhaka, he said.
Doctor Badrul Ahsan, referring to a CT scan report of Rahman, said he was out of danger.
Local police said they were unaware of the accident.