A group of hackers have attacked the websites of the Australian police and Reserve Bank.
The row has heightened diplomatic tensions between the allies and sparked protests in Indonesia.
Indonesia has suspended military co-operation with Australia and recalled its ambassador over the allegations.
A top Australian adviser has also come under fire for several tweets critical of Indonesia’s handling of the row.
Reports of the spying allegations came out in Australian media from documents leaked by whistleblower Edward Snowden.
The leaked documents showed that Australian spy agencies named Indonesian President Susilo Bambang Yudhoyono, the first lady, the vice-president and other senior ministers as targets for telephone monitoring, Australian media said. (read more about this event here)