The move brings Australia in line with the United States, which has restricted Huawei and compatriot ZTE Corp from its lucrative market for similar reasons.
The government said on Thursday that national security regulations typically applied to telecom carriers would now be extended to equipment suppliers.
It did not identify the Chinese firm, but an Australian government official said the order was aimed at Huawei and precluded its involvement in the network.
Huawei's Australian arm said on Twitter on Thursday that the action was an "extremely disappointing result for consumers".
China's commerce ministry said in a statement that Australia had made a wrong decision that would have a negative impact on Chinese and Australian companies.
Australia had previously banned Huawei, the world's largest maker of telecommunications network gear, from providing equipment for its fiber-optic network and moved to block it from laying submarine cables in the Pacific.