Scholes previously managed League Two side Oldham Town in February last year but resigned after just seven games after winning one, losing three and drawing three matches.
Salford City are unbeaten in their five league games this season, winning two and drawing three of their matches to sit fifth on the League Two table.
Salford City are co-owned by Scholes and his former Manchester United teammates Gary Neville, Phil Neville, David Beckham, Nicky Butt and Ryan Giggs.
A club statement read: "Salford City Football Club announces that manager Graham Alexander has left the club with immediate effect. The club met with Graham this morning and after discussion have agreed to part company.
"The club would like to thank Graham for his contribution and all his hard work. In his first season he guided the team to Wembley, resulting in promotion to League 2 and in his second season he reached the Leasing.com Trophy final.
"The club would like to wish him all the best and success in the future.
"First team coach, Chris Lucketti, will also leave the club.
"Paul Scholes will act as the interim head coach while the club looks to secure a new manager. Warren Joyce, currently in isolation, will join Paul once he is able to."
Salford are away at Port Vale in League Two this weekend.
