The opening bell on Wall Street saw shares down by 3%, driven lower by worries over whether the club can appoint the right replacement for the most successful manager in English football history.
His successor will be the key figure at a business laden with almost £370 million of debt and tightly controlled by its US majority owners, the Glazer family.
The club, which trades under the MANU ticker on Wall Street, announced his departure while US markets were closed, but shares slipped on opening as investors digested the impact of the 71-year-old's departure on one of sport's most successful franchises.
In the prospectus to its 2012 stock market flotation, Manchester United warned: "We are highly dependent on members of our management, coaching staff and our players.
"Any successor to our current manager may not be as successful as our current manager."
Shares in the club have surged 34% since floating in August at 14 US dollars (£9) per share, closing on Tuesday evening at 18.77 US dollars (£12.11).
The Glazers bought the Premier League football club for £790 million in 2005 in a controversial deal that enraged fans because they put in just £300 million of their own money and loaded the club with debt.
The club's most recent annual results showed total revenues of £320.3 million for the year to the end of June 2012, down 3.3% on a year earlier.