Woodward has been a target of offensive chanting by United fans in recent matches due to his role in the club’s declining fortunes on the field over the past seven years.
In a statement, United said: “We know that the football world will unite behind us as we work with Greater Manchester Police to identify the perpetrators of this unwarranted attack.
“Anybody found guilty of a criminal offence or found to be trespassing on this property will be banned for life by the club and may face prosecution.
“Fans expressing opinion is one thing, criminal damage and intent to endanger life is another. There is imply no excuse for this.”
A video released on social media showed a flare being thrown over the gate to Woodward’s Cheshire home.
According to the Daily Mirror the attack was carried out by a group of 20-30 balaclava-clad United fans.
