The case is part of a wider question of where Nelson Mandela will be buried when he dies.
The criminal charges add to an ongoing civil suit being waged between Mandla, a member of parliament, and 16 family members.
The network of relatives accuse him of moving the remains of three of Nelson Mandela's children from a cemetery in Qunu village to the town of Mvezo, in the rural Eastern Cape province.
Nelson Mandela was born in Mvezo and Mandla is the head of the tradtional council there.
"Members of the family have opened the case," said Eastern Cape police spokesman Mzukisi Fatyela.
"The docket will be sent to the senior public prosecutor for further investigation."
Continue After The Break.

Relatives have accused Mandla of carrying out exhumations in secret, so he could set up a museum in Mvezo and make a profit.
The family wants the remains back in Qunu, the family's ancestral village, where it is believed Nelson Mandela wishes to be buried when he dies.
A court last week said Mandla has until Wednesday to put the remains back in their original place, but he is fighting the order.
Police would not confirm who laid the charges against Mandla.
Nelson Mandela himself remains in critical, but stable, condition in a Pretoria hospital, according to relatives and the government.
The issue of moving bodies is highly sensitive in the local culture, particularly because gravesites are seen as sacred ground where relatives go to pray and confer with their ancestors.
Court orders relocation of disputed Mandela family remains
A South African court on Tuesday ordered the return of the remains of three of Nelson Mandela's children to his ancestral village, following a bitter family feud linked to the eventual burial site of the ailing anti-apartheid hero.
A judge in the southern city of Mthatha ordered Mandela's eldest grandson Mandla to transfer the remains by 3:00 pm (13:00 GMT) on Wednesday.
Mandla allegedly had the graves moved to Mvezo, about 30 kilometres (18 miles) away, without the rest of the family's consent in 2011.
Mandela, who remains critically ill in what is now his fourth week in hospital, had expressed his wish to be buried in Qunu, and his daughters want to have the children's remains transferred so they can be together.
Previously the grandson has argued that Mandela should be buried at his birthplace Mvezo, where Mandla holds court as clan chief.
The court order was issued in response to a request by 16 relatives of the revered leader.
"I now rule that the respondent complies with the order to return the remains by 3:00 pm on Wednesday," said Judge Lusindiso Pakade.
The remains belonged to Mandela's eldest son Thembekile who died in 1969, his nine-month-old infant Makaziwe who passed away in 1948, and Mandla's own father Magkatho who died in 2005.
Omo Oodua Blog, AFP, dpa