The 23-year-old Holland international sprained his ankle in a 2-1 win over Ternana and risks missing Sunday's trip to newly-promoted Livorno.
A medical update posted on Roma's official website read: "Kevin Strootman has undergone medical tests that have revealed a sprain to his left ankle. We shall discover the prognosis in the next 48 hours.
"In the meantime the player is receiving all the necessary treatment at Trigoria so he can make the best recovery."
Strootman, who has 19 caps for Holland, joined the Giallorossi from PSV Eindhoven for 17million euros in July and scored against an MLS All-Stars side in a pre-season friendly victory held in Kansas City.