They are due to appear in court later.
Nigerian newspaper Punch reports that the police raided a hotel in Lagos State on Saturday afternoon and says the hotel was cordoned off while the investigation was carried out.
Homosexual acts are punishable by up to 14 years in jail in Nigeria, while gay marriage and displays of same-sex affection are also banned.
Chris Ewokor, BBC Africa, Abuja
Nigeria has an influential Christian evangelical movement in the south and strong support for Islamic law in the north, both of which oppose homosexuality.
Since Nigeria passed a law criminalising same sex marriage and gay organisations in 2013, law enforcement agents have cracked down on people suspected of homosexuality. However, arrests are infrequent as homosexual people live in hiding.
Gay people live in fear and cannot openly express their sexual orientation. They are not protected by any law so they face discrimination.
Northern states under Sharia - Islamic religious law - have the death penalty for people convicted of same-sex offences which in other states carry a 14-year jail term.
This is not the first arrest for engaging in acts of homosexuality but so far prosecutions have never ended in prison.
Same-sex relations are explicitly banned in 72 countries, according to the International Lesbian, Gay, Bisexual, Trans and Intersex Association (ILGA).
The number of states that criminalise same-sex relations is decreasing annually, though, with Belize and the Seychelles repealing such laws last year.
Nigeria is one of a small number of countries which has gone against a global trend.
The country has had a ban on gay relationships since 1901, and in 2013 also outlawed same-sex marriages, gay groups and shows of same-sex public affection.
More than 40 men have been arrested in Nigeria over the weekend for performing homosexual acts, police say.