Barcelona confirmed the injury through their website and official social media handles minutes after the match and stated that their captain would be ruled out for at least three weeks.
Messi scored their second goal with a shot from outside the area in the 12th, about 10 minutes after Phillipe Coutinho opened the scoring.
Messi had one deflected wide in the period that followed as chances continued to arrive, and it was not a surprise that the Argentine doubled Barcelona's lead in the 12th minute.
It will be interesting to see how Barcelona fare without him given just how instrumental he is.More news: Trump Cites China Nuclear Buildup In Vowing To Abandon Treaty With Russia
With an global break to come in November, the hope is for Messi to return when Atletico Madrid travel to the Camp Nou on November 24.
Suarez was screaming for a penalty before half-time when he fell under a cynical off-the-ball challenge from Daniel Carrico, but the referee's attention had been on Nelson Samedo, who squandered the opportunity with a terrible shot into the side-netting.
Julen Lopetegui is under intense pressure at the Bernabeu after Madrid's third defeat on the bounce to Levante.
Madrid had practically given up defending its 2016 league title after only three wins in nine matches from October to January.