Rights activists say Malawi has one of the world's highest rates of child marriage, with some girls as young as 9 or 10 married off - even though the marriage age was previously set at 16.
The new law carries a 10-year prison sentence for anyone who marries under the age of 18.
Mutharika, who took longer than expected to okay the law after heated debate, had now "assented to the bill which has become law", said parliamentary speaker Richard Msowoya.
A coalition of local and international NGOs had promoted the bill, saying child marriage "traps girls, their families and communities into a cycle of inter-generational poverty" in the small southern African nation.
"Most of them are forced by their parents into early marriages," said Milliam Chilemba, director of the Foundation for Civic Education and Social Empowerment.
"Many parents cannot afford to pay [school] fees for their girls and they opt to marry off their children to relieve themselves of the burden," Chilemba told AFP.
She said cultural beliefs also played an important role: "Once they reach puberty, parents consider their girls as adults ready for marriage."
Half of Malawi's 15 million people live below the poverty line.
Mutharika told reporters recently that previous governments were "afraid to table the bill in parliament after the process to have the bill started 15 years ago."
But as a "listening government, I am going to decide what is good for the people of Malawi and act accordingly", he said.
The United Nations late last year adopted a resolution calling on governments to stop child marriages.
About 15 million girls worldwide become child brides each year, and more than one in three were married off before the age of 15, according to the UN children's Fund.