Sjafrie Sjamsoeddin along with the chiefs of the army, navy and air force will not attend the show, Indonesian military spokesman Iskandar Sitompul said.
Sjamsoeddin, a retired lieutenant general, also cancelled a lecture he was to give at a Singapore university.
Sitompul said he believed Singapore pulled the invitations of the 100 lower-level officers because of Indonesia's decision to name a new naval frigate the KRI Usman Harun after two marines who killed three people and injured another 33 in a 1965 bombing in Singapore during the conflict between Indonesia and Malaysia, to which Singapore belonged at the time.
''We regret the cancellation since we have good relations on the technical level,'' Sitompul said. ''We should not mix this with politics.''
Indonesian marines Usman Haji Mohamed Ali and Harun Said were executed in Singapore in 1968 and their bodies returned to Indonesia, where they were honoured as national heroes.
Singapore lodged a complaint last week about the naming of the vessel. Indonesia maintains its position that the decision was in accordance with its own procedures and assessment to honour its servicemen.