Eric Aniva, from the southern district of Nsanje, was held after giving a media interview confessing to have slept with the girls for a fee of between four and seven dollars, paid by each of their families.
The little-known local practice lasts three days and is performed in southern Malawi by men known as "hyenas" at the request of a girl's parents after her first menstruation.
The ritual is believed to train girls to become good wives and to protect them from disease or misfortune that could fall on their families or their village.
In a BBC interview broadcast last week, Aniva confessed to being infected with HIV and sleeping with at least 100 girls without using protection.
More From This Section
"Some girls are just 12 or 13 years old, but I prefer them older," he said.
"All these girls find pleasure in having me as their hyena. They actually are proud and tell other people that this man is a real man, he knows how to please a woman."
It was unclear over how many years Aniva had been a "hyena".
Aniva should "be investigated for exposing the young girls to contracting HIV and further be charged accordingly," Mutharika added.
"Harmful cultural and traditional practices cannot be accepted."
The sexual cleansing ritual is also performed on bereaved widows in Nsanje district to exorcise villages of evil spirits or to prevent another death occurring.
Aniva, who has two wives and was reported to be in his 40s, said a "hyena" was selected by the community based on good morals and that custom did not allow him to use condoms.
"I had to do it for the sake of my parents. If I'd refused, my family members could be attacked with diseases -- even death -- so I was scared.