The 49-year-old was considered a key figure in the start-up of the controversial European Super League.
"I am extremely proud to have served United and it has been an honor to work for the world's greatest football club for the past 16 years," Woodward said.
He joined the club after advising Malcolm Glazer's takeover in 2005, slowly rising up the ranks after serving in the commercial and media relations department. Woodward had no previous experience in football.
The announcement of his departure comes as plans for the breakaway European Super League begin to fall apart. Several founding members, including Manchester City and Chelsea, are preparing documentation to leave the ESL, which has drawn widespread condemnation from the football community since it was formed on Sunday.
United players reportedly voiced their displeasure with the club's hierarchy during an emergency meeting Monday and expressed anger over a lack of communication. A source told The Athletic that the players felt "exposed by the club, uninformed, and as though the club didn't bother to fill them in or consult the players over career-influencing changes."
Midfielder Bruno Fernandes appeared to speak out Monday on Instagram, writing, "Dreams can't be bought." On Tuesday, Marcus Rashford tweeted the following quote from former United manager Sir Matt Busby: "Football is nothing without fans."
Defender Luke Shaw also expressed concern that a closed-circuit Super League could negatively "impact the sport that I and millions of others love," adding that the opinions of fans and players "should always be counted."
United announced themselves as one of the 12 founding members of a breakaway Super League last weekend. Club co-chairman Joel Glazer said the ESL would "ensure world-class competition" and increase "financial support for the wider football pyramid." In a joint statement with the other clubs, United said the ESL would provide €10 million in solidarity payments over a 23-year period. But the statement didn't provide specifics or details as to how clubs outside of the ESL could gain entry.
A handful of former players, including ex-United defender Gary Neville, attacked the proposal and called the Glazer family "scavengers" for profiting off the club and its history.
"I've stayed quiet on the basis that it's still Manchester United, you can still watch the lads play, I can be happy and sad, I can still watch football in this country, they take dividends out, I can live with that slightly, but what I can't live with is attacking every single football fan in this country," Neville said on Sky Sports.
"They have stepped over the mark. They are scavengers and need booting out of this football club and booting out of this country. We have got to come together. It might be too late - there'll be people at Manchester United, fans 15 years ago who will say it's too late. It's never too late, we have got to stop this. It is absolutely critical we do."