The Australian Defence Force (ADF) said it used a "small radioactive training source" during war games across Sydney between April 27 and May 29.
It said the exercises involved the ADF, US forces, Australian Federal Police and NSW police.
The exercises were based on tracking weapons of mass destruction, it said.
"At no time during this exercise was any danger posed to the general public," the ADF said in a statement on Friday.
"There was no uranium used during this activity. A small radioactive training source was used."
It said small radioactive training sources are those classified by Australian Radiation Protection and Nuclear Science Agency as being below specified thresholds of radioactivity, which allows them to be used in defence training exercises.
"There was a qualified ionising radiation protection officer with the source at all times," it said.
Ms Rhiannon on Friday said the public had been deliberately "kept in the dark" about the exercises and called on the federal and state governments to place more detail on the public record.
"The government needs to justify why these exercises had to use radioactive material," Ms Rhiannon said in a statement on Friday.
"Military exercises are needed but why should the public be exposed to radioactive material?"
