Following the incident, Dhankar accused the police of being "supportive of the handful of protesters".
The protestors staged the demonstration at hospital more near Domkal Girls' College where the Governor attended a function on Wednesday.
Over a 100 Trinamool supporters stood on both sides of the road waving the black flags when Dhankhar's car was passing the area.
Some of the protestors also carried placards on which were written "go back".
Dhankhar, however, seemed unpurturbed as he rolled down the windows and smilingly waved at them.
Later, however, the Governor in a tweet tagged Chief Minister Mamata Banerjee while lashing out at the police and dubbed the demonstration "orchestrated".
He also alleged that the police were "totally absent" at the collage programme venue.
"@MamataOfficial. At Domkal police was supportive of the handful of protesters while being totally absent at the place where I inaugurated the Domkal Girls College. Orchestrated," the post read.
But in another tweet, where he again tagged the Chief Minister, Dhankhar said he had received a "memorable tumultuous welcome" at the function.
"@MamataOfficial. A memorable tumultuous welcome as I inaugurated the new building of DOMKAL GIRLS COLLEGE. A senior leader and veteran MLA Anisur Rehman and others received me. The emotive enthusiastic reception by girl students was very touching," the tweet raid.
Countering Dhankhar, a state minister denied that the police were supportive of the protestors and said they ensured the protestors could not go near him.
"The police were not there to support the protestors, but they were there to ensure the protestors could not go near him (Dhankhar)," said minister of state for health and senior Trinamool Congress leader Chandrima Bhattacharya.
"The police were there to ensure the governor's security. It is unfortunate that he has been habitually criticising the government without any basis. In the process, he has failed to maintain the sanctity of his chair," she said.
Dhankhar has had constant run-ins with the state's Trinamool Congress government on multiple issues ever since he arrived here in late July to take over the crucial constitutional post.
( With inputs from IANS )