The Italian Rugby Federation, however, said it would appeal the suspension imposed by World Rugby.
Meanwhile the Italians have named a side with nine changes following defeats by Japan and the All Blacks..
In an interview with Sky Sport after Italy's 47-17 thrashing in the Nations Championship last week, Quesada said referee Luc Ramos was "super poor" and the margin of their defeat was made bigger by the actions of the referee.
The Argentine coach also slammed the scheduling of Italy's games, after they began their campaign with a 27-10 defeat by Japan in Tokyo, before flying to Wellington to face New Zealand.
In a statement, World Rugby said, "an automatic two-match suspension has been issued to Gonzalo Quesada, which includes a ban on all match-day activity, including being present in the stadium, as a result of comments made in broadcast."
Quesada, who has the right to appeal, was suspended following the introduction of a new rule this month by World Rugby called the Match Official Abuse Sanction Process.
The process applies across elite competitions and is designed to protect match officials.
The Italian team changes include a first Test start for Giulio Marini, a return to fullback for Lorenzo Pani, a place on the wing for Monty Ioane and Paolo Odogwu's first appearance in the new competition.
Italy are at the bottom of the northern hemisphere standings in the Nations Championship after their two losses.
ITALY: Lorenzo Pani, Louis Lynagh, Juan Ignacio Brex, Paolo Odogwu, Monty Ioane, Paolo Garbisi, Alessandro Garbisi, Ross Vintcent, Michele Lamaro (capt), Riccardo Favretto, Federico Ruzza, Giulio Marini, Marco Riccioni, Gianmarco Lucchesi, Muhamed Hasa Reserves: Pablo Dimcheff, Danilo Fischetti, Ion Neculai, Andrea Zambonin, Alessandro Ortombina, Alessandro Fusco, Giacomo Da Re, Leonardo Marin.
