"You were just getting a wee bit naughty at the end there, so just watch yourself. You still might get a slap even though you're a woman," the Scot was filmed telling Sparks over questions she asked in an interview.
The exchange was captured on a mobile phone camera and published by the tabloid newspaper Daily Star on its website. Both parties appeared to be laughing during the conversation.
The BBC said at the time that Moyes and Sparks had spoken about the exchange and resolved the issue between themselves.
Moyes made a public apology soon after the footage was published, saying he made the remarks "in the heat of the moment" and that he "deeply regrets" them.
"David Moyes has been fined £30,000 in relation to comments he made," the FA said in a statement. "It was alleged his remarks were improper and/or threatening and/or brought the game into disrepute.
"He denied the charge. However, it was found proven following an Independent Regulatory Commission hearing."
Moyes resigned as manager of Sunderland last month after the northeast club were relegated from the Premier League.
(Reporting by Simon Jennings in Bengaluru; editing by Mark Heinrich)
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