The 29-year-old left the field in the 75th minute of the 2-2 draw on Friday night and will play no part in Tuesday's clash with Malta.
His setback is cause for concern amongst the medical staff at Roma, who are already monitoring injuries to both Dodo and Federico Balzaretti.
But while that pair are making marked improvements, the club's medical specialist Michele Gemignani has spoken of his concerns over De Rossi's condition.
"We are a little worried about De Rossi," Gemignani told Roma Channel.
"A clearer evaluation will be made tomorrow, at the moment this is the injury that concerns us the most."