Mr Chakma submitted his resignation to Chief Minister Lal Thanhawla on Monday. The chief minister's office sent the letter to the governor on Tuesday.
The governor accepted the resignation of Mr Chakma today, the sources said.
In his resignation letter, Mr Chakma said that four Chakma students who qualified for MBBS seat under the state quota, were denied the quota in medical colleges across the country by the state Higher and Technical Education department and two of the students belonged to his constituency.
"Remaining in the council of ministers might create uneasiness to maintain the glory of democracy in our state where all of us should feel at home under your dynamic leadership irrespective of caste, creed and religion," he said.
Earlier, the NGO Coordination Committee had urged the Chief Minister to sack Mr Chakma before August 25 and threatened to launch an agitation if Chakma remains a minister.