Scholes, who won 11 Premier League titles with United, retired from playing in 2013.
He became a part-owner of Salford City in 2014 alongside former Manchester United team-mates Gary and Phil Neville, Ryan Giggs and Nicky Butt.
Scholes was charged by the FA in April after it was alleged that he placed 140 bets on football matches between 17 August 2015 and 12 January 2019.
The FA have also warned him as to his future conduct after they revealed the bets the former midfielder had placed.
Scholes, who was also ordered to pay £1,800 in legal fees, placed eight bets on Manchester United during a period when Giggs and Butt were employed by the club.
He also placed a bet on Valencia, then managed by Gary Neville, beating Barcelona.
And another eight bets were put on FA Cup ties, though it was after Salford City had been knocked out.
An independent regulatory commission found no evidence that Scholes was in a position to influence those matches.
Indeed, none of the matches Scholes bet on had involved Salford City.
In total, Scholes placed £26,159 on bets and made a profit of £5,831.
In a statement, Scholes said: “I would like to apologise and I understand and fully accept the fine imposed by the FA.
“It was a genuine mistake and was not done with any deliberate intention to flout the rules.
“I wrongly believed that as long as there was no personal connection between me and any of the matches that I bet upon, then there would be no issue.
“However I understand now that this is not the case and I should have taken steps to verify this at the time.”
The 44-year-old placed his bets using Paddy Power and Bet365 accounts, with the former being deactivated by the bookmaker.
It was Paddy Power who shared the information with the FA after notifying Scholes in November that he was potentially in breach of FA rules.
But Scholes then tuurned to Bet365, placing two bets on matches involving Oldham Athletic, who he would later go on to manage.
There was no evidence though to suggest Scholes had a “connection” with Oldham that would “aggravate matters”.