England fly-half Smith suffers injury scare ahead of Six Nations
With fly-half Owen Farrell ineligible for selection after signing with French club Racing 92, Smith's absence would "definitely be a blow," England attack coach Richard Wigglesworth told British media.
"It wasn't a big incident, that's why I was hoping it was nothing much. He was just jogging, but he pulled up and happened to be right next to a physio when he did it by the sideline."
Reports said the 24-year-old was later seen using crutches and was to undergo a scan.
England are already without centres Ollie Lawrence and Oscar Beard and hooker Luke Cowan-Dickie for the match in Rome on Saturday
Coach Steve Borthwick could turn to George Ford at number 10 if Smith is unable to make it, with the uncapped Fin Smith another option.
Borthwick is scheduled to announce his starting line-up on Thursday.