Ronaldo, already been ruled out of Portugal's final World Cup Group One qualifier against Malta on Wednesday, looks certain to miss Real's Champions League Group C match against AC Milan on October 21.
He sprained his right ankle in a match against Olympique Marseille last month and limped off in the 27th minute on Saturday before returning to the Spanish capital for tests.
"A clinical examination and a scan showed the player had suffered a recurrence of the injury to his right ankle," Real said in a statement on their website.
"Estimated time out of action three to four weeks depending on clinical developments," the statement added.
Portugal lie second in the qualifying standings behind group winners Denmark and will secure a playoff berth if they beat Malta at home.
Ronaldo had shown signs of recovery before the Hungary match and on Friday told reporters he was almost fully fit.
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