The forward was carried off on a stretcher in the last minute of Derby's friendly draw against Stoke on Saturday following a challenge by City defender Carl Dickinson.
Boss Nigel Clough said: "We are disappointed for him. He just felt something in his Achilles, I think it was a combination of a kick and the way he fell.
"We will just wait and see what the medical people say but it doesn't look too good at the moment."
Barnes, 20, spent almost 10 months out with a serious knee injury last year. He returned towards the end of December and then joined Fulham on loan but did not make a first-team appearance for the Premier League club.
The move was with a view to a permanent deal but the Londoners did not follow up their initial interest.