Authorities in the North Caucasus region have been jailing and torturing homosexual men, Russian newspaper Novaya Gazeta reported in March.
It said that over 100 gays had been arrested in the Muslim-majority region and that their families had been told to kill them to "cleanse their honour".
The German foreign ministry said that, in the case of one gay man, "a visa was issued and the person was able to come to Germany on June 6," while four more cases were under consideration.
"We are glad we are able to help in particularly difficult cases," said a ministry official.
German Chancellor Angela Merkel in early May urged Russian President Vladimir Putin to investigate the reports of an anti-gay purge and to ensure the safety of gays and lesbians.