Sanctions for Wenger and Nasri were expected after their verbal outbursts at referee Massimo Busacca following Arsenal's last-16 elimination against Barcelona.
More surprising was UEFA's disciplinary panel ruling that Jordan should also be banned for his touchline clash with AC Milan captain Gennaro Gattuso.
Jordan's ban was imposed almost four weeks after UEFA ordered Gattuso to sit out four matches in future European club competitions.
On Thursday, the panel found Wenger and Nasri guilty of improper conduct toward Swiss official Busacca after Arsenal's 3-1 loss in Spain last week.
They must serve the bans in the Champions League or Europa League.
Wenger also was fined ¤10,000 ($14,000). On being charged by UEFA, the Frenchman likened the European football authority to a dictatorship and said he deserved an apology.
Busacca angered Arsenal by sending off Robin van Persie at 1-1 in the 56th minute, with the English side ahead on aggregate. He judged that the Netherlands forward deserved a second yellow card for deliberately kicking the ball away immediately after being ruled offside.
Barcelona eventually advanced to the quarterfinals 4-3 on aggregate.
UEFA suspended Jordan from duty when Tottenham next plays in its marquee competition on April 5 or 6. Tottenham will discover its quarterfinals opponent in the draw on Friday.
Jordan, aged 59, clashed verbally and physically with Gattuso when his team won 1-0 at the San Siro on Feb. 15.
UEFA banned Gattuso for assault when he headbutted Jordan after the final whistle.
Tottenham advanced after the teams drew 0-0 in the return with Jordan assisting manager Harry Redknapp in the dugout.
Jordan, Wenger and Nasri can appeal their punishments within three days of receiving detailed reasons for the UEFA decisions.