The charge relates to Boro's 1-1 Championship draw with Blackburn Rovers at the Riverside Stadium on November 29.
With the hosts leading 1-0 deep into stoppage time, Rudy Gestede bundled in a last-gasp equaliser to earn Rovers a share of the spoils.
Middlesbrough were furious that the goal was allowed to stand, having believed there were fouls on both defender Ben Gibson and goalkeeper Dimi Konstantopoulos in the build-up.
Karanka reacted angrily on the touchline and was sent to the stands by referee Mark Clattenburg, and will now serve a suspension for the visit of Championship leaders Derby County on Saturday.
"Following an Independent Regulatory Commission hearing today, Middlesbrough head coach Aitor Karanka will serve a one-match touchline suspension with immediate effect," an FA statement read.
"Karanka, who was also fined £2,000, admitted an FA charge of improper conduct in relation to his behaviour during stoppage time at the end of the game against Blackburn Rovers on 29 November 2014."
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