Singh, whose clothes were splattered with blood, was treated at a hospital in the district where the doctors stitched the wound. He was later brought to Kolkata and admitted in the private Apollo Gleneagles hospital.
A hospital spokesperson said Singh, who had a scalp injury, was admitted in the ICU for observation under neurosurgeon S.N. Singh.
Before being brought to Kolkata, Singh told media persons that he was thrashed by the Barrackpore Police Commissioner Manoj Verma while protesting along with his party workers against Trinamool workers who had vandalised his car.
"Democratic protest movements are not being allowed in West Bengal. There was an attack on me, and my car was damaged. After that, the people were protesting peacefully. But then came Barrackpore Police Commissioner Manoj Verma who baton charged me directly... on my head. He abused and attacked me," said Singh, sporting a bandage on his head.
Denying that Singh was baton charged, the state police in a statement said he got the head injury "from a brick thrown by his supporters".
Accusing Singh and his son Pawan Kumar Singh - the BJP MLA of Bhatpara - of leading hooligans, and "forcibly" blocking road in Jagaddal area of Barrackpore, the statement said that Verma, along with other officers, had requested Singh not to cause inconvenience to general public.
"He didn't listen and provoked his supporters to attack police. Several policemen including the Commissioner are injured in the attack by hooligans.
"A pistol has been snatched and a bomb was thrown aiming at police from the roof of the house of Arjun Singh," the statement said.
The police claimed the situation has been brought under control.
Describing Singh - a former Trinamool Congress MLA from Bhatpara who switched over to the BJP and won the LS polls on the saffron party's ticket earlier this year - as a "ruffian", state minister and Trinamool's district President Jyotipriyo Mullick alleged that he and his associates had "attacked the police".
According to eyewitnesses and locals, the incident was related to the capture of a political party office in Shyamnagar.
After Singh won the Lok Sabha contest from Barrackpore, a number of Trinamool party offices were captured by the BJP, and a violent turf war is still going on between the two parties in the area.
Singh and his loyalists headed to the spot after coming to know that one of the party offices captured by the BJP had been recaptured by Trinamool.
They removed the Trinamool festoons and claimed to have recaptured the party office.
Clashes broke out between the BJP and the Trinamool and Singh's car was vandalised and its windshield broken. The BJP workers started protesting on the road, thereby triggering clashes between them and the police.
Singh's injury sparked a strong reaction in the BJP which called a 12-hour bandh in the Barrackpore Lok Sabha constituency on Monday.
BJP's Working President J.P. Nadda charged the Trinamool with attempting to "capture" his party's office in North 24 Parganas district and perpetrating violence on Singh and his son.
"It is highly condemnable. By resorting to such ill-means, TMC has been murdering the democracy time and again in West Bengal," Nadda tweeted.
"This violence shows helplessness of TMC and @MamataOfficial against the things changing for better in the state. Each and every karyakarta of BJP is pained today and will respond to this in the days to come.
"The West Bengal police acting on the wish and command of the TMC in hurling these brutal atrocities is a clear evidence of how the state machinery is being misused for political vendetta by the @MamataOfficial," he added.
BJP national General Secretary, Organisation, B.L. Santosh condemned the "high-handedness of state police.
BJP General Secretary in-charge of West Bengal Kailash Vijayvarigya, party's state chief Dilip Ghosh, and national Secretary Rahul Singh were among those who visited Singh at the hospital.
BJP National Executive member Mukul Roy said he has apprised Prime Minister Narendra Modi and Union Home Minister Amit Shah of the attack on Singh and demanded a CBI probe into "the needless violence on an esteemed politician".
( With inputs from IANS )