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The game is part of a six-day training camp in north Wales before Wales fly to the southern hemisphere to play Tonga on 17 June and Samoa on 24 June.
The Test against Tonga will be staged in another country, due to concerns over the the stadium in Nuku'alofa.
Forwards coach Robin McBryde will lead the trip while Warren Gatland and Rob Howley are involved in the British and Irish Lions tour of New Zealand.
Wales trained at the Colwyn Bay ground in preparation for the 2015 Rugby World Cup while Wales Under-20 have played there in the Six Nations.
"We are delighted to be heading to north Wales this summer," McBryde said.
"The facilities are great at Parc Eirias and will provide us with the exactly what we are looking for in terms of a training camp.
"Not only will the match be hugely important for the squad off the field, it will be a great spectacle to see RGC line up against the Welsh side and a huge opportunity for all those players."
McBryde will be joined on the tour by regional coaches Danny Wilson, Matt Sherratt and Stephen Jones who will be part of his backroom staff.
Apart from any Lions who are selected, Wales will field a full strength side against RGC 1404, who are fourth in the Premiership table and knocked holders Llandovery out to reach the Welsh Cup semi-finals earlier in March.
Wales will play Welsh Premiership side RGC 1404 at Parc Eirias on 2 June.