The Spain international lasted just nine minutes of Wednesday's 2-1 Liga victory over Sevilla before being replaced by Nacho.
Ramos has subsequently undergone examinations that have confirmed the severity of his injury.
A statement on Real's official website read: "Following tests carried out on Sergio Ramos by the Real Madrid medical service at the Sanitas La Moraleja Hospital, the player has been diagnosed with a torn hamstring in his left leg. His progress will be monitored."
Ramos' injury provides a further defensive setback for Real ahead of Saturday's Liga derby with rivals Atletico Madrid at the Vicente Calderon.
Fellow centre-back Pepe has been absent for the past month with a rib injury, while full-back Marcelo is suspended - although Real hope to have the yellow card he picked up against Sevilla rescinded.
Elaborating on Ramos' injury and his options in defence, coach Carlo Ancelotti said: "The injury to Ramos is important - five weeks.
"I've confidence in Raphael Varane and Nacho, they are very good players, very enthusiastic, very motivated. They will do well tomorrow, no problems.
"We do not know yet on Marcelo, we are waiting on the final judgement. We still hope the card can be overturned.
"At left-back we can use either Fabio Coentrao or Alvaro Arbeloa."
Real are also without James Rodriguez for the clash with Spanish champions Atletico, the Colombia international having suffered a fractured metatarsal against Sevilla after scoring the opener.
Rodriguez's absence is offset somewhat by the return of superstar Cristiano Ronaldo from a two-match suspension.
And Ancelotti stated the Portugal international is in prime condition ahead of the mouth-watering fixture.
"Ronaldo is motivated as always," he added. "He has enjoyed his week's work very well and is in top condition."
