Tutu confirmed the investigation of granddaughter Ziyanda Palesa Tutu in a statement released yesterday by the Desmond and Leah Tutu Legacy Foundation.
"We are naturally distressed and deeply saddened," Tutu said in the statement. The foundation said it "hopes and prays that the family will soon be able to put this incident behind it."
Tutu did not divulge details of the criminal charge. But police in Western Cape province, where Desmond Tutu is based, indicated in a statement that his wife Leah had initiated the complaint.
The retired archbishop said his statement was a response to comments posted on social media by his granddaughter.
Ziyanda Palesa Tutu said on Twitter on Tuesday that she was "regrouping" and "will be handing myself in on Friday." She describes herself on Twitter as Desmond Tutu's first grandchild, a qualified wine judge and a writer from Johannesburg with "controversial" political and religious views.
Desmond Tutu was awarded the Nobel Peace Prize in 1984 for campaigning against South Africa's white racist rulers at the time.