City striker Alex Fletcher, 23, was taken away in an ambulance after the incident in the opening minutes of the match.
A decision was taken to abandon the game at Bath’s Twerton Park, with the score at 0-0.
Bath tweeted: “This evening's game has been abandoned and will be played at a later date.
“Everyone at the club is deeply saddened by tonight's events and it has been agreed that the game will not resume. Our best wishes and thoughts are with Alex Fletcher.
Fletcher collided with an advertising hoarding in the early stages of the game and we are awaiting an ambulance at Twerton Park.
We will update you all as soon as possible, but for now all of our best wishes are with Alex.
— Bath City FC (@BathCity_FC) November 8, 2022
“We will update supporters on Fletcher's condition at the earliest opportunity.”
South London club Dulwich sent their best wishes to the player and his club.
A statement read: “Due to the serious injury sustained by Alex Fletcher, both teams have agreed to abandon the game.
“For now the most important thing is the safety and recovery of Alex, and from everyone connected with Dulwich, we wish him a speedy and full recovery.”