The Romania international picked up the injury during a training session and could miss his side's next 12 games in Serie A and the UEFA Europa League.
A statement on the club's official website confirmed that Radu sustained the problem on Wednesday, and had been diagnosed with a rupture of his medial knee ligament after medical examinations.
The 26-year-old will have his leg in a brace to stabilise his knee for three weeks, but he is not expected back in training for eight weeks.
Radu joined Lazio from Dinamo Bucharest in 2008 and has made 130 league appearances for the club - including both matches in Serie A so far this season.
Striker Sergio Floccari will join Radu on the sidelines after he was ruled out with a thigh injury, however the 31-year-old is only expected to be out of action for a week.
Lazio have got their campaign under way with a 2-1 victory over Udinese sandwiched by heavy defeats to Juventus, 4-0 in the Supercoppa Italiana and 4-1 in Serie A last time out.
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