The match, scheduled for June 17, could now be moved to New Zealand.
"The difficult decision to move the match was made after it was confirmed that ground works in relation to the redevelopment of the national stadium in Nuku'alofa were running behind schedule, with the result that the pitch may not be fit for purpose in time," the WRU said in a statement on their website (www.wru.co.uk).
"Given the significant logistics involved in hosting an international touring test team, it was agreed by all parties that it would be prudent to move forward with alternative venue arrangements to ensure that the test match could still take place in June at an appropriate facility.
"Discussions are taking place with alternative venues to host the match on the same weekend in June."
New Zealand media reported on Saturday that Auckland was being considered as a possible venue for the match, given the large Tongan community in New Zealand's biggest city.
Tongan supporters produced one of the more memorable moments of the run-up to the 2011 Rugby World Cup when they caused gridlock around Auckland International Airport as they welcomed their team.
Wales, who will be without their British and Irish Lions players, also also face Samoa in Apia on June 24.
(Reporting by Greg Stutchbury in Napier; Editing by Nick Mulvenney)
