He was sent off during United's 3-0 thumping by Tottenham Hotspur at Old Trafford in the 42nd minute for a high challenge on midfielder James Maddison.
Fernandes was set to miss United's Premier League fixtures against Villa on Sunday, Brentford and West Ham United before his red card was overturned.
"Bruno Fernandes will be available for Manchester United's next three games following a successful claim of wrongful dismissal," the Old Trafford club said in a statement.
United are 13th in the Premier League with seven points from six matches.