“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 simply no excuse for this,” a statement issued from United after the incident read.
It is believed that Woodward, his wife and two daughters were not in the house at the time of the incident.
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United are currently in fifth place in the Premier League, six points off Champions League places.
They face Manchester City in the Carabao Cup semi-final second leg on Wednesday, hoping to overcome a 3-1 deficit.