The Six Nations-winning coach was cleaning windows when he lost his balance and fell almost 10 feet onto concrete, leaving him in leg casts and requiring surgery to reconstruct his right heel.
Assistant coach Rob Howley will take over the day-to-day reins temporarily, although Gatland is still expected to be fit enough to lead Wales on their tour to Australia this June.
"We all wish Warren a speedy recovery from the injuries he has suffered in this extremely unfortunate accident," said WRU chief executive Roger Lewis.
"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."
Gatland has been in charge of Wales since 2007, winning two Six Nations Grand Slams and reaching the World Cup semi-final in that time.