The City midfielder has pulled a groin muscle and will play no part in the 1st Round tie at Ashton Gate on Tuesday night.
"Scott over-stretched for a ball and certainly won't play against Barnet," manager Brian Tinnion told the clubs official website.
"It's too early to say how long he will be out, but it's bad luck because he was doing well."
Tony Grant, who signed for City at the end of last week but played no part against Vale, is the most likely debutant for the injured Brown.