But police have denied the claim of intimidation, saying officers gave the man and his companion "a lecture" after they were "caught in the act" in a public toilet.
The organization Genderdoc-M said the 26- year-old man, whose name it did not disclose, and his companion were briefly detained by two policemen on December 6 in a Chisinau park that is a popular meeting place for gay men.
Genderdoc-M representative Angela Frolov told RFE/RL that the incident was witnessed by a Genderdoc-M activist who said one of the policemen was carrying an automatic rifle.
The witness said the two officers used extremely rude and homophobic language and threatened to take the two young men to the police station and to disclose their sexual orientation to their families and employers.
Genderdoc-M said its activist persuaded the police officers to let the two men go.
But Frolov said that several hours after the incident, the man called his mother from a pay phone, told her that he was gay, and then hanged himself in his aunt's house where he was living.
In a statement, police denied the claim of intimidation.
It alleged that the two men were "caught in the act" in the park's public toilet after police followed up on a complaint from two women who had been told by their children there were gay men there.
"The policemen simply gave them a lecture," the statement said.
Genderdoc-M issued its statement to coincide with International Human Rights Day and draw attention to what it says are frequent cases of police harassment and blackmail of gays.
Frolov said the few unofficial "cruising areas" for gays in Chisinau are deliberately targeted by policemen who demand bribes from gay people in exchange for not telling their families, employers, or teachers about their sexual orientation.
Homosexuality was decriminalized in Moldova in the 1990s but is still largely taboo in a conservative, mainly Orthodox Christian society.
Genderdoc-M has led a so-far unsuccessful bid to hold a gay rights march in Chisinau.