Tigers prop Ayerza, who has been nominated for a place in the IRPA World Team of the Year, will win his 47th international cap at the Millennium Stadium in Cardiff.
Matera, who made his Tigers debut in the Aviva Premiership game away to London Wasps in October, makes his 10th Test appearance in the Pumas back row alongside captain Juan Manuel Leguizamon and Julio Farias Cabello.
Former Tigers wing Horacio Agulla also starts while Lucas Gonzalez Amorosino is among the replacements.
Blaine Scully is away on international duty with USA as they prepare to play Georgia at the Rustavi Rugby Stadium on Saturday. The Eagles are still to name their team but, if selected, Scully will win his 14th international cap.
Meanwhile, former Tigers prop Martin Castrogiovanni will make his 100th international appearance for Italy in Saturday’s match against Fiji (2pm GMT).
Castrogiovanni, who made 146 appearances for Tigers before moving to Toulon in the summer, will reach a century of Tests for the Azzurri alongside captain Sergio Parisse.