The two militants, who carried out the attack, were also killed.
"Five jawans have been martyred and seven have been injured," a senior police officer told reporters at the spot.
He said it was not clear whether there were two or three militants who hurled grenades and opened indiscriminate firing at the CRPF camp.
"Two fidayeen (suicide militants) were neutralised and searches are going on," the officer said.
He said the group affiliation and identity of the militants killed in the incident was a matter of investigation.
The CRPF camp at Bemina is surrounded by the Police Public School and many government buildings.
However, the school was closed due to strike called by separatists in support of their demand for return of mortal remains of Parliament attack convict Mohammad Afzal Guru.
This is the first suicide attack in Kashmir in the last three years with the last such incident taking place in January 2010.
No militant outfit has claimed responsibility for the attack so far.
On March 2, militants had shot dead two policemen in Handwara area of Kupwara district.