A number of demonstrators targeted Woodward’s house in Cheshire last Thursday to show their anger at the club’s involvement in the failed European Super League.
The group caused damage to the gates at the front of the drive, before leaving, with no one at home at the time.
Cheshire police have told Sky Sports News they weren’t alerted to the incident.
Earlier that day, a separate group of around 20 fans, carrying banners, broke into United’s training ground to protest against the Glazer family’s ownership.
Woodward, who joined United in 2005 and has been in his current role since 2012, will step down at the end of 2021, the club announced last Tuesday.