FIFA said its disciplinary committee had found the German guilty of breaching rules on "offensive behaviour and fair play". He was also fined 7,000 Swiss Francs ($7,440) and 1,000 Swiss Francs in costs.
The former Borussia Dortmund and Bayern Munich coach was captured by television cameras sticking his middle finger -- known in German as the "Stinkefinger" -- at the official at the end of the 1-1 draw.
The usually unflappable Hitzfeld only raised his finger for a split second and the referee did not appear to see the incident which became a big talking-point in staid Switzerland.
Switzerland lead Group E with 10 points from four games in the European 2014 World Cup qualifying competition. He will miss the matches away to Cyprus on March 23 and at home to the same opponents on June 8. (Writing by Brian Homewood, editing by Justin Palmer)