Robert Mugabe Junior, 31, one of three children of the former Zimbabwean leader, has been accused of destroying cars at a party last weekend in the country's capital Harare.
The estimated value of the damaged property is $12,000 police said.
The arrest followed his friend's report of the incident to local authorities.
Mugabe Junior's father, Robert Mugabe, died at 95 in 2019, two years after he was compelled to leave the president's office.
The presidential post was then taken by his former right-hand Emmerson Mnangagwa who is still leading the country.
After the former president passed away, his family accused Mnangagwa of betraying the Southern African country's long-time leader, which resulted in deteriorated relations between them.
Despite that, Mugabe Junior took part in the president's rally last year and was invited back to the ruling Zanu-PF pParty, thus reconciling with Mnangagwa.