The embassy condemned the "deplorable behaviour" and said the staff member would be strongly disciplined.
Israel's ambassador was summoned by the Singapore government over the incident, local media report.
Singapore's foreign ministry said the "misuse" of its flag was considered a serious offence.
Images of the flag draped over a table at a party allegedly hosted by the diplomat were posted online on Monday by a user who said a police report had been filed.
He accused the foreign party host of having "no respect for our country and our flag".
In a press statement, the Israeli embassy said it "was appalled to learn of the deplorable behaviour displayed by one of its junior staff members and expresses its sincere apologies".
Israel has apologised after a junior diplomat working at its embassy in Singapore reportedly used the country's flag as a tablecloth at a party.