"This is an outrage. We're turning back the clock when there's ample evidence to show that we should not condone child marriages," said Ivy Josiah, executive director of Women's Aid Organization, a rights group.
Muslims make up about 60 percent of the 28 million population of the Southeast Asian country and fall under family and criminal laws individually drafted and run by each of the country's 13 states. Non-Muslims come under federal civil laws.
The chief minister of Malacca, Mohammad Ali Rustam, said permission would only be granted after consent by the teenager's families as well as the state Islamic courts.
"For the state government, this is the best step to deal with the problem of abandoned babies and unwed pregnancies," he was quoted as saying by the Utusan Malaysia newspaper.
"This is a knee-jerk reaction, and such policies should not be carved out by state religious authorities but the federal Ministries of Women, Education, and Health," said Josiah.
The number of underage pregnancies in Malaysia rose to 111 in the first four months of this year from 107 in 2008, according to government numbers.
Recent cases of babies being abandoned by their unwed mothers have led the Malaysian government to set up its first baby "hatch," where mothers can drop off unwanted children anonymously.
(Reporting by Razak Ahmad; Editing by David Chance)