Northern Ireland are due to play Cyprus in Nicosia next week and the friendly is scheduled to go ahead as planned at the moment.
However, all First Division fixtures in Cyprus have been postponed this weekend after the Cyprus Referees Association said its members would not attend any of the matches.
The car of top Cypriot official Leontios Trattos was damaged in the explosion, which caused no casualties.
And the bombing is reportedly being seen as an isolated incident, which is unconnected to international football.
A statement from the Cyprus FA said: "Such incidents are beyond any boundary of logic."
IFA chief executive Patrick Nelson said: "I have been in touch with the president of the Cyprus FA and we will continue to monitor developments."