One suspect, identified as Milembe Suleiman, a procurement officer at a gold mine in Geita Region, has already been arrested.
Police are now searching for a second unidentified woman who was shown in the video clip wearing an angagement ring and "flaunting" it after allegedly being engaged by Milembe.
According to the Sexual Offences (Special Provisions) Act of 1998, homosexuality is a criminal offence in Tanzania, where suspects convicted of having “carnal knowledge of any person against the order of nature” could face the possibility of life or a minimum of 30 years in jail.
Milembe was arrested after the roughly two-minute video clip was widely circulated in social network platforms showing her purportedly hosting an engagement party for several guests, where she was seen kissing and embracing her female partner.
"I can confirm that a Tanzanian woman is under police custody over that video clip. We will issue more details later after we conclude our investigation," Geita police chief Mponjoli Mwabulambo told reporters.
The arrest of the woman in Geita was thought to be the first arrest of a lesbian suspect in the recent crackdown.
The clip drew condemnation on social media platforms in the socially conservative nation, with some Tanzanians condemning the alleged engagement party as immoral.
“Both of them should be arrested. Why did the woman accept an engagement ring from another woman?” Cosmas Alele, a resident of the northwestern town of Kagera said on Twitter, writing in Kiswahili.
"The law should take its course to put an end to this shame. Does this mean that there are not enough men to go around or was it just the work of Satan?" Ally Lissu, a Dar es Salaam resident, said on Twitter.
President John Magufuli's government has stepped up a crackdown against homosexuality since coming into power in November 2015 and has since arrested several suspects.
The government threatened in June to arrest and expel activists, as well as deregister all non-governmental organisations that campaign for gay rights.
Authorities in Dar es Salaam raided a suspected "gay meeting" at a hotel in October and arrested at least 12 suspects, including Tanzanians, South Africans and a Ugandan and deported the foreigners.
The government also deregistered a Tanzanian NGO after accusing it of hosting the meeting and promoting same-sex relationships.
The country's health ministry banned NGOs last year from distributing free lubricants to gays as part HIV/AIDS control measures.
Some health experts warn that shutting down HIV/AIDS outreach programmes targeting homosexuals could put the wider population at higher risk of infections.
Around 1.4 million Tanzanians are living with HIV, the virus that causes AIDS, according to government estimates.