The tech giant had engaged in "false, misleading or deceptive conduct" by knowingly hosting the ads for bogus cryptocurrencies, a regulator said.
The US company could face financial and other penalties.
Meta is yet to comment but has previously said it is committed to keeping scammers off its platforms.
The Australian Competition and Consumer Commission (ACCC) says the ads in question used Facebook's algorithms to target susceptible users and featured bogus quotes by Australian celebrities.
Identities used without permission included former New South Wales Premier Mike Baird, prominent TV host David Koch and millionaire entrepreneur Dick Smith.
"The essence of our case is that Meta is responsible for these ads that it publishes on its platform," ACCC chairman Rod Sims said in a statement on Friday.
The legal action, filed in the Federal Court of Australia, alleges Meta did this knowingly and failed to prevent the scams even after objections were raised by celebrities.
"In one shocking instance, we are aware of a consumer who lost more than A$650,000 (£360,000; $480,000) due to one of these scams being falsely advertised as an investment opportunity on Facebook. This is disgraceful," Mr Sims said.
Last month, Australian billionaire Andrew Forrest launched a criminal case against Meta over fake ads that used his image.
While Dr Forrest accuses the tech giant of breaking anti-money laundering laws, the ACCC's case is about alleged breaches of consumer law or a separate regulatory act.
Meta - which also owns Instagram and Whatsapp - made $115bn in global advertising revenue in 2021.
