Healy withdrew from Leinster's starting XV shortly before kick-off of last weekend's 40-7 Heineken Cup win over Northampton and had already been declared unfit for Saturday's return fixture in Dublin.
The two-month time-frame means the opening fixtures against Scotland and Wales appear too early for his return, but he could feature against England on February 22.
"Cian had ankle surgery on Wednesday so he's unavailable for about eight weeks. He's doing good but he won't play for a while," Leinster coach Matt O'Connor said.
Healy had surgery on his left ankle during the summer to correct an injury sustained on the British and Irish Lions tour to Australia and has made just four appearances for Leinster this season.