Police spokesman Superintendent Billy Jones confirmed a 34-year-old man had been arrested at 1:45 am near Cape Town's seafront, but said "we are not at liberty to implicate people by name until they have appeared in a court of law."
Jones said the man, reported by the SAPA news agency and state SABC radio as being Gibbs, was pulled over for speeding.
"A breathalyzer test was conducted within the prescribed time and the man detained at 3:45 at the Sea Point Police station," he told AFP.
Gibbs was released on 500 rand (62 dollars/40 euros) bail, and would appear in Cape Town magistrates' court on June 27.
The South African, who was left out of the Test squad currently on tour in India but remains a regular in the one-day team, plays for the Cape Town-based Cobras franchise.
He was recently signed up to play for Hyderabad in the inaugural Indian Premier League, a multi-million dollar Twenty20 event which begins on April 18, in a deal worth 575,000 dollars.
No stranger to controversy, Gibbs was banned for six months over his role in a match-fixing scandal and he was also caught smoking cannabis during a tour to the West Indies.