Turkish officials had no immediate comment.
Turkey, a secular Muslim country, has been a key ally to Israel, but relations have cooled over Turkish Prime Minister Tayyip Erdoğan's outspoken criticism of Israel's three-week offensive in the Hamas-ruled Gaza Strip in December and January.
The military exercise, scheduled to begin on Monday in Turkey, takes place every few years with the aim of improving international aerial cooperation, the Israeli military said.
"The exercise has been postponed as a result of Turkey's decision to change the list of participating countries, thus excluding Israel," a military statement said.
An Israeli political source said Turkey had rejected Israeli participation and postponed the drill indefinitely after other nations, including the United States and Italy, refused to take part without Israel's air force.
Turkey and Israel have enjoyed close military cooperation, including Israeli air force training in Turkish air space. The two countries also share intelligence and have strong trade ties, including the sale of important military equipment.
Relations were strained after Erdoğan publicly criticised Israel over the Gaza campaign and walked out on Israeli President Shimon Peres at the World Economic Forum in Switzerland in January.
A UN report last month found that both the Israeli armed forces and Hamas militants committed war crimes in the Gaza war, but it was more critical of Israel.
A Palestinian rights group says 1,417 Palestinians, including 926 civilians, were killed in the war. Israel has said 709 Palestinian combatants were killed along with 295 civilians and 162 people whose status it was unable to clarify.
Fourteen Israelis were killed during the conflict which Israel launched with the declared aim of curtailing cross-border rocket attacks from the Gaza Strip.
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