The 48-year-old Kiwi's return to Wales has been delayed as he recovers from the incident on Easter Monday.
WRU chief executive Roger Lewis said: "We all wish Warren a speedy recovery from the injuries he has suffered in this extremely unfortunate accident."
Gatland was cleaning windows when he lost his balance and fell around 10 feet onto concrete, taking the full impact on his heels. He suffered multiple fractures to the right calcaneus and also a fracture to the left calcaneus.
Consequently, he is in leg casts and requires surgery to reconstruct his right heel.
The injury is not expected to have any major impact on the continuing preparations for Wales' matches in June, although the WRU have put plans in place for some coaching to be managed internally by Gatland's assistants.
Assistant coach Rob Howley will oversee day-to-day management of the coaching staff in Wales, while Gatland will continue to receive information primarily from Howley, Robin McBryde, Shaun Edwards and Neil Jenkins as they observe and monitor squad players and potential players over the next few weeks.
Lewis has approved the plan for temporary injury cover and has indicated that, although there is no current requirement for any of the staff to be appointed caretaker head coach, he and Gatland have agreed to recommend to the WRU Board that Howley would fill the role if required.
Lewis continued: "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."