Gatland, who led Wales to the RBS 6 Nations title this year, fractured both heels during the accident at his house in Waikato, New Zealand in April and missed Wales' summer tour of Australia, with Rob Howley taking charge.
Gatland, who will lead the British and Irish Lions tour Down Under next year, is expected to be hospitalised for a few days but it is not thought to be a set-back.
"The operation to his right heel, which was broken in his much-documented accident, will see Warren enter hospital on Friday," read a statement.
"The procedure will entail treatment to an area of damaged and blistered skin.
"It is expected he will spend a few days in hospital after the procedure."
Meanwhile, Wales' decision to travel to Japan for a two-test series next June will help the Asian champions bridge the gap to the world's top sides, according to coach Eddie Jones.
Jones, the former Australia coach, will welcome the reigning RBS 6 Nations champions next summer for clashes in Osaka on June 8 and Tokyo on June 15.
Wales last played in Japan 11 years ago, winning both games of a two Test series, and defeated the Brave Blossoms 98-0 at the Millennium Stadium in 2004 and 72-18 at the same venue three years later.
Wales will again be heavy favourites to claim a series whitewash but after winning just one game in seven World Cup appearances, Jones insists they need regular challenges like this.
"Back in May, the Welsh under 20s beat Japan by at least 90 points," he said.
"There is a big gap between the level of rugby played in Japan and international rugby.
"These two tests are so important. But two are not enough. You can't play low level teams and improve. We need ten games like this a year."