The 12 women and eight men were picked up in a hotel where they were receiving training about HIV/Aids education programmes.
Earlier this year, authorities banned many private health clinics from providing HIV/Aids services, saying they encouraged gay sex.
Homosexuality is a crime in Tanzania.
Regional police commander Hassan Ali Nasri said on state television: "They are implicated in homosexuality. We arrested them and are busy interrogating them. The police cannot turn a blind eye to this practice."