The Scotland international sustained the injury in the 3-0 defeat to West Brom, which left Sunderland rooted to the foot of the Premier League table.
Fletcher had the chance to score but landed awkwardly after volleying over the bar and Di Canio lamented the setback.
"He missed the chance but the big issue is that he got an injury to his shoulder," he said.
"We sent him to the hospital because we want to discover the extent.
"It was painful for him and his shoulder was still out. They could not touch him."
Fletcher scored 11 goals for Sunderland last season before having to undergo ankle surgery, which kept him out for the last two months of the campaign.
And Di Canio warned that he could be absent for a similarly prolonged period this time.
"He came back very good from his ankle injury but he will probably have to be out for more than a few weeks," he said.
"It is very bad at the minute. Our main man misses a chance and gets an injury.
"He is a predator in the box and we don't have this kind of player at the minute. We have strikers but not someone with his characteristics."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.