They had been scheduled to train in Madrid on Monday morning before flying later in the afternoon but changed their plans.
"The club didn't want to run even the smallest risk and opted to postpone training...to make the most of a gap in the air space that would allow them to fly direct to Hamburg," Atletico said on their website.
Atletico wanted to avoid the kind of trek their Europa League semi-final opponents Liverpool had to take last month.
Liverpool were forced into a 2000-kilometre odyssey to arrive in Madrid for their semi-final first leg because of the airspace restrictions caused by the volcanic eruption in Iceland.
They took a train to London and the Eurostar rail service to Paris, caught a train to Bordeaux and flew the last leg to Madrid.
Rafael Benitez's side lost 1-0 at the Calderon and went out on away goals despite a 2-1 win at Anfield.
Atletico coach Quique Sanchez Flores has taken 23 players to Hamburg, including Portugal midfielder Tiago and striker Ibrahima who are both ineligible to play.
Atletico take on Fulham in the Europa League final on Wednesday.
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