Dhankar, who cut short his visit to Delhi to visit the Apollo Gleneagles Hospital where Singh is now under observation, termed the incident as "serious" and said the state needed a peaceful atmosphere and not violence.
"I had been to Delhi. I cut my visit short. I came from Delhi this morning because of this very serious incident," he told reporters after emerging from the hospital.
The Governor said the Lok Sabha member from Barrackpore had some "serious problem" on Sunday night" at the hospital.
"I am a worried man at the moment. ... The state of West Bengal needs a peaceful atmosphere. State of West Bengal does not need violence, state of West Bengal must be on path of progress.
"Holding this constitutional position, my object is we must believe in rule of law, and we must believe in peace. We must avoid violence... I am in pain looking at all this violence," he said.
Dhankar, who took oath as Governor on July 30 after his predecessor Keshri Nath Tripathi's stint came to an end, stressed the need for a system where everyone is disciplined.
"We must have a system where everyone acts in a disciplined manner and without violence. I feel pain when something happens to teachers, doctors, lawyers and journalists," he said.
Singh, admitted to the hospital on Sunday after he was allegedly hit in a baton charge by the police at Shyamnnagar in North 24 Parganas district, got shifted to a cabin on Monday from the ICU.
He has alleged that he was hit with on his head by Barrackpore Commissioner of Police Manoj Verma while protesting along with his party workers against Trinamool workers who had vandalised his car.
Denying the charge, the state police in a statement said he got the head injury "from a brick thrown by his supporters" and accused the MP of provoking the BJP workers to attack the cops.
( With inputs from IANS )