The 23-year sailor hailing from Tamil Nadu was found dead yesterday on board INS Talwar in Mumbai, Navy sources said.
A Board of Inquiry has been ordered, they said in Delhi.
His family has alleged that the sailor had complained about not being granted leave.
In the recent past, there have been instances in the defence forces where cancellation of leave has been cited as the reason for suicides.
In June last year, soldiers and officers in an Army unit in Samba were engaged in a face-off after the suicide by a jawan there.