Salah, who has hit five league goals for the Giallorossi since making his move from Chelsea permanent, is expected to be out until the New Year after being stretchered off early in the second half of Roma's 2-0 derby win on Sunday after his right ankle bent inwards under the impact of Lulic's stamp.
Although fractures were ruled out on Sunday, further tests on Monday revealed Salah has "sustained a grade II ligament damage to his right ankle," according to a club statement.
Salah is confirmed to miss the Pharaohs' anticipated World Cup qualifiers against Chad on 14 and 17 November.
In a post on Facebook, Lulic wrote: "I'm sorry Mohamed Salah, it wasn't my intention to hurt you. I hope to you see back playing soon."
Roma coach Rudi Garcai said: "Tackles like that don't belong, even in a derby. The players need protection."
"You've seen the pictures, I'll say no more."
Roma's win left them in third spot in Serie A, one point behind leaders Fiorentina and second-placed Inter Milan following their respective wins away to Sampdoria and Torino.
Roma signed the international winger this summer on loan from Chelsea before revealing that they made the deal permanent for a reported fee of 20 million euros.
Salah scored five goals in 11 league appearances this season.
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