France international Benzema was replaced by Jese Rodriguez as Madrid drew 0-0 at Etihad Stadium, leaving everything to play for in the second leg at the Santiago Bernabeu on Thursday.
Madrid on Thursday confirmed the nature of the 28-year-old centre-forward’s injury but did not provide a timeframe on his likely return.
“After tests today at University Hospital Sanitas La Moraleja, the player Karim Benzema has been diagnosed with [a] myofascial strained right hamstring,” the club said in a statement.
Los Blancos are away to Real Sociedad in La Liga on Saturday, with head coach Zinedine Zidane also troubled by the fitness of star forward Cristiano Ronaldo, who sat out of the match against City due to a thigh problem.
“Hopefully they can be in the second leg but we have to take it day by day for them,” Zidane said of the attacking duo after the stalemate in Manchester.
“We’re going to try and get them fit for [the second leg], that’s our plan but I can’t assure you of anything right now. We obviously want them back.”
Madrid are third in the Liga table, one point behind Barcelona and Atletico Madrid, who are level on 82 points in first and second place respectively.