The front row duo have been released by the Irish management, following a request from the Barbarians to make two players available.
Hooker Varley's involvement comes after an encouraging season in Munster colours, during which he played 22 times for his native province including six appearances in the Heineken Cup.
Ulster prop Court has added to his international experience this season with run-outs for Ireland against Fiji, Italy and France.
The New Zealand Barbarians' match against the Maori, at Northland Events Centre in Whangarei (kick-off 4.35pm local time/5.35am Irish time) is on the same day as Ireland's Test against the All Blacks.
The New Zealand Barbarians, founded in 1937, are an invitational side and based on the concept of the world famous Barbarian FC. They wear scarlet red jerseys, white shorts and red socks and have a white leaping lamb as their symbol.
Coached by Bryce Woodward, the NZ Baa Baas' line-up includes six All Blacks, one of them being Blues prop John Afoa who will be tried out in the hooker role at the request of the New Zealand management.
Woodward said: "We are all about to be part of something special and for these guys, it's a real privilege to be asked to share in the tradition and honour of assembling and playing with the New Zealand Barbarians.
"We're very excited that in the spirit of the Barbarians tradition, two of the Irish internationals are joining us."
Court and Varley will rejoin the Irish touring party on Sunday in Rotorua, where next Friday's New Zealand Maori v Ireland XV fixture will be held.
NEW ZEALAND BARBARIANS (v New Zealand Maori): Jared Payne (Northland); Bryce Heem (Auckland), Rene Ranger (Northland), Ben Smith (Otago), Fetu Vainikolo (Otago); Colin Slade (Canterbury), Alby Mathewson (Wellington); Jamie Mackintosh (Southland), John Afoa (Auckland), Charlie Faumuina (Auckland), Josh Bekhuis (Southland), Kevin O'Neill (Waikato), Scott Waldrom (Taranaki), Alando Soakai (Otago) (capt), Pater Saili (Auckland).
Replacements: Damien Varley (Garryowen/Munster/Ireland), Tom Court (Malone/Ulster/Ireland), Andrew van der Heijden (Auckland), Dean Budd (Northland), Rhyan Caine (Northland), Lachie Munro (Northland), Daniel Bowden (Auckland).