The 51-year-old had a personal hearing in front of an Independent Regulatory Commission on Friday after accepting the Football Association's charge of using "abusive and/or insulting words towards a spectator" during their 3-1 defeat by Liverpool.
Pearson had refused to apologise to the supporter despite calls from the Leicester City Supporters' Club to say sorry.
The statement from the FA read: "Following an Independent Regulatory Commission hearing, Nigel Pearson has been fined £10,000, will serve a one-match touchline suspension, and warned as to his future conduct, subject to any appeal, after he admitted using abusive and/or insulting words towards a spectator.
"The sanction will not come into effect until the end of the appeal period.
"The Leicester City manager was charged following his side's game against Liverpool on 2 December 2014."
A statement from Leicester stated Pearson and his representatives have requested written reasons for the sanctions.
It continued: "The club has concluded an internal review of the incident during the Liverpool fixture and considers its own review to be closed."
Pearson, who usually watches matches from the stands anyway, was bullish after the incident.
He said: "I've had run-ins with fans in the past and in the heat of the moment these things happen.
"I'm not going to repeat what happened on either side
I'm very keen to protect myself and my players
I'm more than happy to stand up for myself in that situation.
"If people were offended then that is regrettable
But there is no need to apologise to somebody of that ilk."
Leicester are on an 11-game winless run and are bottom of the Barclays Premier League ahead of Saturday's trip to high-flying West Ham.
Source : PA
Source: PA