Ziyanda Palesa Tutu, Mr Tutu's eldest grandchild, has been accused of property damage, according to South African police.
"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 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".
Police said: "This office can confirm that a malicious damage to property case was opened for investigation by the complainant against her granddaughter." The case was opened on 7 May, police said.
A few hours later she reportedly followed-up a post that said she was "too emotional" to speak to the media.
She wrote: 'Bn receiving requests 4 interviews regarding this @TheDesmondTutu Leah Tutu thing. I'm 2emotional right now bt will talk when I'm ready.'
In an interview with local news website News24, Miss Tutu would not confirm what she was being charged with, but said she believed her grandparents could have handled the matter privately.
She pointed out that they were the ones with the money and the power, the website reported.
