The 22-year-old was sentenced to 12 months in prison at Guildford Crown Court on Friday for actual bodily harm, with a concurrent four-month sentence for common assault after pleading guilty to both charges.
A statement on the club's website read: "We were informed on Friday afternoon that Joshua Payne had received a custodial sentence after pleading guilty in relation to two charges following an incident that occurred in Guildford in May 2012.
"In the light of this, notice to terminate the contract of the player will be given forthwith. The club cannot condone or excuse such behaviour.
"Our players and staff are important role models for our next generation of supporters and will be reminded of their behavioural responsibilities to the club at all times."
Following Saturday's 4-2 victory over Rochdale, boss Dean Holdsworth said: "As a manager and a person I'm upset at what's happened, I love the lad. He's had this hanging over his head for a long time.
"The players love him, it's a shock for everybody. I told the players that if they're going to do anything then Josh is part of it - he's part of us. Our thoughts are with is family, and we've just got to get on with our jobs."