“The current trend of unresolved cases of violence against women and girls in Zimbabwe, including marriages of minors, cannot continue with impunity,” the UN said in a statement on Saturday.
The girl’s death on 15 July has put the spotlight on the practice of child marriage within Zimbabwe’s Apostolic Church, which often rejects medicine and hospital treatment.
Her family has said that the baby survived the birth and was doing well, local media report.
The circumstances that led to the death and subsequent burial are under investigation by the police and the country’s state gender commission.
An online petition calling for “justice for Memory Machaya” has so far received more than 57,000 signatures.
Women and girls were “not seen as fully human, with individual rights… to control our own bodies” she wrote on Twitter.
By law, Zimbabwean girls are allowed to get married at the age of 18, while 16 is the age of sexual consent.
But some families believe child marriage can provide financial benefits.
Many child brides hope marriage will provide the opportunity to go to school. However, young girls typically end up falling pregnant soon after, or being kept at home to carry out household chores.