Read: UP governor quits, other UPA picks may follow soon
The resignation of 63-year-old Kumar came days after Union home secretary Anil Goswami telephoned some of the governors, appointed by the previous UPA regime, to step down after the Narendra Modi government assumed charge.
Uttar Pradesh governor BL Joshi and Chhattisgarh governor Shekhar Dutt put in their papers last week.
Kumar, a former IPS officer who had served as director of Central Bureau of Investigation, was appointed as Nagaland governor in March 2013.
Kumar was CBI director when the agency had arrested BJP general secretary Amit Shah in connection with the Sohrabuddin Sheikh alleged fake encounter killing case in Gujarat.
All the three governors who have resigned so far are either former IPS or IAS officers. Joshi is a former IPS officer and Dutt is a former IAS officer.
However, no governor with a political background has stepped down as yet.
Earlier on Wednesday, home minister Rajnath Singh did not rule out the possibility of appointment of some new governors before the budget session of Parliament beginning July 7.
"I will not rule out anything now...I will be able to tell you only after 3-4 days," he said.
Sources said the government was considering appointing some BJP veterans as governors in around 10 states.