It comes after Pearson accepted a Football Association charge following an incident with a supporter in City's 3-1 Premier League loss to Liverpool.
The 51-year-old was called arrogant by the chairman of a Leicester supporters group after he refused to apologise.
He can appeal against the decision and the sanction will not come into effect until the end of the appeal period.
Pearson declined to reveal what was said during the altercation with the supporter, but said he felt it necessary to protect his players and himself from abuse.
He was also warned about his future conduct by an Independent Regulatory Commission panel.
Pearson has been manager of Leicester since November 2011 and guided them to the Championship title last season.
However, they have struggled in 2014-15, are bottom of the Premier League table and have not won a game since beating Manchester United 5-3 on 21 September.
Leicester City boss Nigel Pearson has been given a one-game touchline ban and fined £10,000 for insulting a fan.