"The passing of this titan is a sad loss for the game," said Cricket South Africa CEO Pholetsi Moseki, who paid tribute to Koertzen's "selfless dedication and commitment."
South Africa's Algoa FM radio station reported that Koertzen and three other people were killed in a head-on collision near the town of Riversdale in the Western Cape province.
Koertzen was returning to his home in the Eastern Cape province after playing in a golf tournament when the crash happened, the station said.
Umpire and long-time colleague Aleem Dar paid tribute to Koertzen: "It is a very big loss foremost for his family and then for South Africa and cricket. I stood in so many games with him. He was not only very good as an umpire but also an excellent colleague, always very cooperative on field and also always willing to help off the field. Because of the way he was, he was also well respected by the players."
Australian great Jason Gillespie wrote: "RIP Rudy- very good umpire, nice man. Thoughts are with his family and friends."
Indian star Virender Sehwag wrote: "Vale Rudi Koertzen! Om Shanti. Condolences to his family. Had a great relation with him. Whenever I used to play a rash shot, he used to scold me saying, "Play sensibly, I want to watch your batting".