Three people died and 33 were injured in the attack on MacDonald House, a bank building in Singapore's Orchard Road shopping district.
The then-Indonesian President Sukarno had opposed the formation of the Federation of Malaysia, that included Singapore, by British colonial rulers in 1963.
Low-level fighting and bombings continued over ownership of several territories until a peace deal was signed in 1966, by which time Singapore was an independent city state.
The marines were captured after the bombing and hanged in Singapore 1968, but decorated posthumously in Indonesia after their remains were returned for burial.
Relations began improving after Singaporean Prime Minister Lee Kuan Yew visited Jakarta in 1973 and paid his respects at the two men's graves in Jakarta's Kalibata Heroes Cemetery.
The recent war of words began after Indonesia announced it had named a refurbished frigate after the two marines, Usman Haji Mohamed Ali and Harun Said.
Chan Chun Sing, Singapore's second minister of defense, said in a written statement last week that he was "disappointed" with Indonesia's decision to name the warship after the marines.
"I am also disappointed with the reactions of the Indonesian leaders who have spoken on this issue thus far. The statements reflected either a lack of sensitivity, a lack of care for bilateral ties, or both."
The biennial airshow, formerly known as Changi International Airshow, is a major gathering of civilian and air defense companies and buyers in Southeast Asia.
But Indonesia's top defense officials, including Deputy Defense Minister retired Lt. Gen. Sjafrie Sjamsoeddin and head of the armed forces Gen. Moeldoko, won't attend the Singapore Airshow, The Straits Times reported.
The leaders pulled out Sunday ahead of scheduled meetings with Singaporean officials this week, the Times reported.
The Jakarta Post reported Indonesia's defense attache in Singapore conveyed the cancellation via text message to Singaporean officials.
"The text said the cancellation was decided after taking into consideration public opinion in Singapore," Indonesian Defense Ministry spokesman Brig. Gen. Sisriadi Iskandar said.
However, the Indonesian air force's Jupiter Aerobatic team show went ahead as planned Sunday.
An editorial in the Post Saturday urged more "sensitivity" by Jakarta towards its smaller neighbor, which, like Indonesia is a member of the Association of Southeast Asian Nations.
The diplomatic row between Indonesia and Singapore "is unfortunate and could have been avoided if we had been a little more sensitive toward our neighbor," the editorial said.