European soccer's ruling body found the Manchester United winger guilty of elbowing Russia's Vadim Yevseyev during the 0-0 Euro 2004 playoff first leg draw in Moscow on November 15.
Wales lost the return leg in Cardiff 1-0, thereby failing to qualify for Euro 2004, which means Giggs will miss Wales's first two qualifiers for the 2006 World Cup.
The ban does not apply to friendlies.
Wales boss Mark Hughes said an appeal could be lodged.
"We have the option of an appeal which we have to lodge by Monday," Hughes told the BBC following the 2006 World Cup qualifying draw in Frankfurt, which placed Wales in the same group with neighbours England and Northern Ireland.
"We may consider that but obviously the worry with an appeal is that if you do lose it the punishment could be increased so that will have to come into our thinking."
Giggs lashed out at Yevseyev minutes after being hurt by a strong tackle from the Russian defender during the second half of the first leg match in Moscow.
He avoided punishment from the referee but Russia later complained and UEFA charged Giggs with improper conduct, although he was free to play in the second leg.
Yevseyev scored the winning goal for Russia in Cardiff to book their place at next year's finals in Portugal.
Probably Wales's best player, Giggs will be sorely missed by his country when they embark on their qualifying campaign for Germany 2006 next autumn.
Wales have not qualified for a major tournament since the 1958 World Cup.
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