The 26-year-old is facing up to six weeks on the sidelines after suffering the injury in Leicester narrow win over Sale.
And with England set to kick-off their championship challenge against Scotland on February 4, Flood is unlikely to be fit in time.
Tigers director of rugby Richard Cockerill told the Leicester Mercury: "He (Flood) hurt his knee on Sunday and we initially thought it was just like a dead leg but it swelled up overnight and he went to see a specialist to determine the exact nature of the injury.
"It turns out that he has tweaked his ligaments and is likely to be out for four to six weeks, which is not as bad as we feared at one stage.
"But it still rules him out of the Wasps and Ulster games, which is not great after Manu Tuilagi and Louis Deacon's recent injuries."
"But it still rules him out of the Wasps and Ulster games, which is not great after Manu Tuilagi and Louis Deacon's recent injuries."
Tuilagi is out for four weeks with a hamstring injury, meaning he too is a doubt for the Calcutta Cup clash, while Deacon has been ruled out for three months.
Flood's absence for the start of the Six Nations would open the way for Charlie Hodgson's return at fly-half - although Owen Farrell and Freddie Burns are both pushing for inclusion.
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