Gatland was cleaning windows at the Waihi Beach house in the Bay of Plenty when he lost balance and fell three metres onto concrete, taking the full impact on his heels.
The 48-year-old suffered multiple fractures to the right heel bone and also a fracture to the left one. He is in leg casts and needs surgery to reconstruct the right heel, delaying his return to Wales.
The WRU said the injuries were not expected to have any major impact on the continuing preparations for scheduled Wales matches in June which include a three Test tour in Australia.
Under Gatland, Wales captured the Six Nations title in March, winning all five matches.
Although it could be several weeks before he fully recovers, he is expected to be able to return to active coaching duties before his recuperation is complete.
WRU chief executive Roger Lewis said: "We all wish Warren a speedy recovery from the injuries he has suffered in this extremely unfortunate accident.
"Knowing Warren as I do I can reassure the Welsh rugby public that he has diligently put the people and processes in place to ensure he stays closely linked to what is happening in the game back here in Wales.
"I have spoken to Warren on a number of occasions since his fall and have told him he will lead the tour to Australia unless anything unforeseen happens in the prognosis for recovery we are working to."