According to police, the constable, identified as Panat D. Sangma of the 3rd Meghalaya Police Battalion, was found hanging inside the tent outside the embassy.
The body was found by his colleagues when enquired as he did not turn up for duty.
When asked, a police official said no suicide note was recovered from the place.
Police are investigating to ascertain the exact reason that led to the constable killing himself.
Meghalaya home minister Lahkmen Rymbui said the police man was attached to the Bhutan Embassy and committed suicide on Monday night.
The home minister also told reporters that it is yet to be ascertained as to why the police constable had taken the drastic step to end himself and said the probe is on.
He informed that the body of the police constable has been sent for conducting post-mortem.
The family members of the constable have been intimated about the incident, the minister said.
Stating that every profession is a challenge, the Meghalaya home minister said the duty of the home department is to take care of all the police personnel.