The Pretoria-based Vodacom Bulls, where White is currently director of rugby, say the two-hour operation was successful.
White, 59, complained of debilitating stomach cramps after arriving in South Africa from Wales – where the Bulls had played United Rugby Championship opponents the Dragons – on Sunday.
“It is never nice to see one of our own down, but we are extremely confident that Jake is receiving the best medical attention available, and our team of medical experts will provide him with all the necessary support he will need to make a full recovery,” Bulls chief executive Edgar Rathbone said.
“We would like to thank the hospital team, doctors and all those who rushed to offer their expertise and helped with attending to Jake.”
Rathbone said he had visited White in hospital in Pretoria on Monday.
A statement on the Bulls’ official website read: “While recovering from the operation and going through his rehabilitation programme, White will be taking a brief break from his team duties until February 8.
The coaching team will continue to share the responsibility of leading the team while the director of rugby is away
“At present, the club cannot place a time-stamp on the length of this period, but will be guided by the expertise and advice of the medical staff.
“The coaching team will continue to share the responsibility of leading the team while the director of rugby is away.”
The Bulls tackle Heineken Champions Cup opponents Exeter in Pretoria on Saturday, before visiting Lyon six days later and then facing a URC game against the Scarlets in Llanelli on January 27.