The fire was reported in the lift motor room in the Sir Bobby Charlton stand at about 07:00 GMT.
Sarah Louise Feeney tweeted: "Fire at Old Trafford in South Stand ... Fire alarm going off since 7am and smoke!!!"
Firefighters were at the scene for about 90 minutes. Manchester United said there was minimal damage and no injuries.
In a statement, the club said: "A small electrical fire was identified quickly in the Sir Bobby Charlton stand around 7am today.
"The fire brigade attended and the isolated incident was dealt with quickly and effectively."
An electrical fire broke out at Manchester United's stadium, resulting in smoke being seen over Old Trafford.