The tournament will take place in France from June 10 to July 10.
Giancarlo Abete, UEFA's vice-president since 2011, told Radio24: "We can't exclude the possibility of playing behind closed doors, as we cannot exclude terrorism. If we talked about potentially cancellable games, such as a friendly or a competitive match, they could be moved to another date.
"Obviously this would not be the case. But we are talking about games which are staged for June whereas, today, we are going through a very urgent emergency."
Thirty-four people were killed in the Belgian capital - home to the European Union's headquarters - following explosions at Zavantem Airport and Maalbeek metro station.
Belgium today cancelled another training session ahead of a friendly with Portugal at King Baudouin Stadium in Brussels next Tuesday.