Gardner could be ruled out long-term after being stretchered off during the Owls' 1-1 draw at Middlesbrough - and Jones is hoping scan results do not confirm the club's worst fears.
"It looks like he has torn his Achilles, but we won't know for sure until he has had a scan," Jones told reporters
"He says he felt something kick and that is a similar sensation to a tear.
"But we will hope for the best and assess things properly when he has the scan."
Gardner, a free signing following his release from Crystal Palace in the summer of 2012, has started in all six of Wednesday's matches so far this season.