The Romania international picked up the problem in training and scans have now revealed the extent of the damage.
Lazio confirmed that he had been diagnosed with a rupture of his medial knee ligament and would need to have his leg in a brace for around three weeks.
Radu will then be able to begin his rehabilitation but he is not expected to return to action until early November.
The 26-year-old, who can play at either centre-back or left-back, joined Lazio from Dinamo Bucharest in 2008 and had been linked with a move to Manchester City this summer.
The loss of Radu for the next couple of months will be a major blow to Lazio as they look to push on at the start of the season.
Lazio opened their Serie A campaign with a 2-1 win over Udinese but were then hammered 4-1 by defending champions Juventus.