"The authorities said to them: 'Your son is a homosexual - sort it out or we'll do it ourselves'."
The victim added: "We've always been persecuted, but never like this. Now they arrest everyone. They kill people, they do whatever they want."
The man's name has been suppressed to protect his identity.
Russian officials claim there is no persecution of gays in the republic, despite a Russian newspaper's report that more than 100 men suspected of homosexuality were rounded up and at least three killed.
It comes as German Chancellor Angela Merkel pressured Russia's Vladimir Putin to investigate reports of torture and the persecution of gay men in Chechnya and ensure the safety of LGBT people across the region.
Making her first to Russia in two years, Merkel said she raised concerns with Putin about the reported violent crackdown during a meeting in Sochi on Tuesday.
"I asked President Putin to use his influence to protect these minority rights," Merkel told reporters.
Merkel also raised other human rights concerns, including police breaking up anti-Kremlin protests and a Supreme Court ruling last month banning the Jehovah's Witnesses religious group as extremist, the Telegraph reported.
"I have in my talks with the Russian president indicated how important the right to demonstrate is in a civil society and how important the role of NGOs is," she said.
Putin said Russia's law enforcement officers behaved in a far more restrained manner than colleagues in other European countries.
The reports of Chechnya's gay purge have attracted international attention and condemnation, with America's Ambassador to the United Nations Nikki Haley calling for an investigation.
"We continue to be disturbed by reports of kidnapping, torture, and murder of people in Chechnya based on their sexual orientation and those persecuted by association," Haley said in a statement.
Sarah Kate Ellis, president and CEO of the LGBT rights group GLAAD, described it as a "humanitarian crisis".
"It is beyond horrific for a country to proactively target, arrest, and abuse LGBT people," Ellis said.