Brazilian left back Marcelo and Croatian midfielder Modric underwent tests on Monday after being forced off the pitch during Real's 2-1 home win over Malaga on Saturday.
"Following tests carried out today at the Sanitas La Moraleja University Hospital, Marcelo has been diagnosed with a grade 2 muscle injury in his left hamstring," Real said in a statement.
"Modric has been diagnosed with a strain in his right abductor muscle."
Real did not confirm the length of the absences but Spanish media reported that the duo could be out of action for up to a month.
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They are likely to miss several key games, including Real's Champions League last 16 first leg at home to Napoli on Feb. 15.
Real, already without the injured Pepe, Dani Carvajal and Gareth Bale, visit Celta Vigo on Wednesday bidding to overturn a 2-1 first-leg deficit to reach the King's Cup semi-finals.
Zinedine Zidane's side are one point clear of Sevilla at the top of La Liga with a game in hand.
(Reporting by Adriana Garcia, editing by Ed Osmond)
