Ahmed Msangi, police chief in Tanzania's Mwanza region, said authorities arrested the woman in the northwestern region of Geita and are looking for the other woman and some others seen in the video.
He said "it is just a matter of time" before law enforcement officers arrest the others, adding "the plan is to eliminate the entire chain of people involved or supporting homosexuality for the betterment of the generations."
Homosexual relations are criminalized in Tanzania and the law prescribes jail terms of up to life.
This East African nation has launched a countrywide crackdown against people accused of promoting homosexuality.
Authorities have threatened to deregister NGOs accused of supporting gays.
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