Australia has seen 136 confirmed cases of coronavirus, and three deaths. Morrison acknowledged the stimulus would mean he will not meet an election pledge to balance the country's budget -- a key plank of the party's pitch to voters last year.
Australia's economy had already been limping before the coronavirus hit -- with raging bushfires and drought slowing growth to a stall.
The central bank has repeatedly cut rates to historic lows while warning that the coronavirus outbreak could have "large and long-lasting" effects.
Morrison had on Wednesday announced a separate $1.6 billion war chest to bolster medical services that are likely to come under intense strain as the virus spreads in the coming months.
He is expected to make a rare televised address to the country later on Thursday to speak about the broader challenges faced by the COVID-19 outbreak.