The victim is Topu Debnath, 20, a constable at Biswanath Police Station, hailing from Juri upazila in Moulvibazar district.
Colleagues said Topu tried to commit suicide by shooting himself at the rooftop of the police barrack on Monday evening.
He was rescued and taken to Biswanath Health Complex immediately, they said, adding that he was transferred to MAG Osmani Medical College Hospital after providing with first aid.
Dr Himangshu Lal Roy, deputy director of the hospital, said they sent the policeman to Dhaka around 11pm as his condition was critical.
Farid Uddin, superintendent of Sylhet police, said it is yet to be known why he wanted to kill himself.
Colleagues said he was talking with a woman over mobile phone before making the suicide attempt.