Dier leapt into the stands and was involved in a heated argument with a Spurs fan as stadium security guards attempted to break up the fracas.
An FA statement read: "Eric Dier has been suspended for four matches with immediate effect, fined £40,000 and warned as to his future conduct following a breach of FA Rule E3.
"An independent Regulatory Commission subsequently found Eric Dier's actions to be threatening."
Spurs boss Jose Mourinho said after the match that a fan had insulted Dier's brother, but he did not approve of his player's reaction at the time.
In a news conference on Wednesday, previewing Spurs' clash with Bournemouth, Mourinho said he did not want to comment on the ban.
Asked if Spurs were planning to appeal the decision, Mourinho added: "I don't think so, honestly. Because if you appeal, you have other risks so at least let's start next season without a suspension.
"We all know how it works with FA decisions. You have successful appeals and unsuccessful appeals. I don't think we're going to appeal."
One of the reasons why the case was delayed so long was because Dier's solicitor, Ellen Peart, asked for a Right of Access Request because the police refused to voluntarily provide witness testimony from the fan in which he admitted to "being an idiot."
The case was adjourned for weeks while that information was acquired. England manager Gareth Southgate also provided a character reference, highlighting his "maturity, leadership qualities and close family ties."
The Commission rejected the claim that Dier was just protecting his brother and concluded he went after the supporter despite the fan apologising.
The suspension means that the England international will miss Spurs' trip to Bournemouth on Thursday and the north London derby at home to Arsenal on Sunday.
Dier has featured for 90 minutes as a centre-back in every game since the Premier League restart.
"I think they made a decision when Guendouzi grabbed the other guy by his neck," Mourinho said. "The decision was made in that moment."
The Spurs boss was also unhappy after midfielder Dele Alli received a one-match suspension and £50,000 fine last month after posting an offensive video on social media in which he mocked an Asian man over the coronavirus.
ESPN correspondent James Olley also contributed to this report.