The incident occurred in the final minute of Saturday's 2-2 draw at Ashton United.
After being taken to hospital, the club have confirmed that Benns had suffered "significant ankle damage".
Operating primarily as an attacking midfielder, Benns first joined the club in May.
He has scored six times in 17 appearances this season - topping the club's charts for both goals and games played.
No timescale has been placed on his recovery, although the serious injury is expected to keep him out for a significant period. Benns will also undergo surgery, during which time he will be unable to work.
Bamber Bridge captain Macauley Wilson has subsequently set up a GoFundMe to support his team-mate during the recovery. An initial target of £1,500 was set, with that figure already surpassed.
He said: "As a team, we have decided to raise money for Harry Benns - a fellow team-mate and top lad.
"while we all know it's tough already in this world we live in financially, please donate whatever you can - it will be greatly appreciated."
Click here to donate to the Harry Benns fundraiser.
Photo credit: Bamber Bridge