While Madrid did not specify how long they will be without their captain, reports in the Spanish media claimed he will not be available again in November.
A Madrid statement released on Thursday read: "After the tests carried out today on Sergio Ramos by the Real Madrid medical department, the player has been diagnosed with a strained hamstring in his right leg. His recovery will continue to be assessed."
Zidane will also have concerns over Raphael Varane after the centre-back went off at half-time in France's 4-2 victory against Sweden.
Los Blancos have played 115 LaLiga games without Ramos since he signed from Sevilla in August 2005 and have only lost 10 of those.
Their win percentage when he does not feature is 78.3 percent, compared to 67.1 across his 462 appearances in the top flight.
Madrid have lost two of their past four LaLiga games, as many as in their previous 33 matches in the competition, and they will be looking to stop Villarreal making it seven unbeaten in the league, which would represent their best run since October 2016.