Gibbs became the first man to achieve the feat in a limited overs match, and only the third in history in all forms of cricket, when he launched into Dutch slow left-armer Daan van Bunge in the 30th over.
The brutal big-hitting took Gibbs from 32 at the start of the over to 68 by the end of it.
Van Bunge at least had the minor consolation of helping to dismiss his tormentor when he held a catch in the deep in the next over off captain Luuk van Troost.
Gibbs eventually went for 72 with four fours and seven sixes having faced just 40 balls.
The first man to hit six sixes off an over in a first-class match was West Indian legend Sir Garry Sobers, playing for Nottinghamshire against Glamorgan at Swansea in 1968 with Malcolm Nash the bowler taking the punishment.
Former India all-rounder Ravi Shastri then equalled the feat playing for Bombay against Baroda in 1984.
Gibbs's historic feat will also cost a leading drinks firm one million dollars.
The Johnnie Walker company had already agreed to donate the money to charity in honour of the first player to register the landmark.
Former West Indies skipper Viv Richards had hoped on the eve of the World Cup that six successive sixes would be hit.
"These days we are seeing more and more big totals and sixes being hit in one-day cricket by powerful batsmen with big bats, yet no-one has ever hit six sixes in one over of any international match," said Richards on Tuesday.
"The only people who have ever done it in first-class cricket are our own Gary Sobers and India's Ravi Shastri and to me this tournament, with our traditionally short boundaries, is the time to change that."
Fall of wickets: 1-0 (de Villiers); 2-114 (Smith); 3-219 (Gibbs).
Netherlands: L. van Troost (capt), P. Borren, D. van Bunge, R. ten Doeschate, A. Kervezee, T. de Leede, D. Reekers, J. Smits, B. Stelling, E. Szwarczynski, B. Zuiderent
Umpires: Mark Benson (ENG) and Tony Hill (NZL)
Tv umpire: Steve Bucknor (WIS)
Reserve umpire: Asoka de Silva (SRI)
Match referee: Ranjan Madugalle (SRI)