Reacting to the development, State Education Minister Bratya Basu warned his department would move the Supreme Court against the governor's decision.
The Raj Bhavan opened the cell on August 1, a day after Bose announced such a cell to hear the grievances directly from the affected students in the state.
"The setting-up of the anti-corruption cell means the Governor wants to go on a confrontation course with the state government, " Basu told reporters on Tuesday.
"This move is a direct attempt on the part of the Governor to bring the state higher education under his control.
"This state has a non-BJP government. Such a move is underway in the BJP-run states across the country. But such a move in West Bengal is unprecedented, " said the Education Minister.
"The action taken without consulting the state Higher Education department means he is prejudiced about the establishment being a place of corruption. This is absolutely undemocratic, " Basu reiterated.
Before opening the anti-corruption cell at Raj Bhavan to hear the grievances of the students directly, Bose had opened a "Peace Room" at his gubernatorial office to have complaints related to Panchayat election-related violence.
Over 50 people have been allegedly killed since the Jun 8 announcement of the panchayat polls.
Hundreds were rendered homeless as they sought to escape the wrath of the political rivals in rural Bengal.