The ban - which will not take effect for at least 12 months - could see tech companies fined up to A$50m ($32.5m; £25.7m) if they don't comply.
Prime Minister Anthony Albanese says the legislation is needed to protect young people from the "harms" of social media, something many parent groups have echoed.
But critics say questions over how the ban will work - and its impact on privacy and social connection - have been left unanswered.
This is not the first attempt globally to limit children's social media use, but it involves the highest age limit set by any country, and does not include exemptions for existing users or those with parental consent.
"This is a global problem and we want young Australians essentially to have a childhood," Albanese said when introducing the bill to the lower house last week. "We want parents to have peace of mind."
Having passed the Senate by 34 votes to 19 late on Thursday, the bill will return to the House of Representatives - where the government has a majority meaning it is sure to pass - for it to approve amendments, before becoming law.
The legislation does not specify which platforms will be banned. Those decisions will be made later by Australia’s communications minister, who will seek advice from the eSafety Commissioner - an internet regulator that will enforce the rules.
Gaming and messaging platforms are exempt, as are sites that can be accessed without an account, meaning YouTube, for instance, is likely to be spared.
The government says will it rely on some form of age-verification technology to implement the restrictions, and options will be tested in the coming months. The onus will be on the social media platforms to add these processes themselves.
However digital researchers have warned there are no guarantees the unspecified technology - which could rely on biometrics or identity information - will work. Critics have also sought assurances that privacy will be protected.
They have also warned that restrictions could easily be circumvented through tools like a VPN - which can disguise a user’s location and make them appear to be logging on from another country.
Children who find ways to flout the rules will not face penalties, however.
Polling on the reforms, though limited, suggests it is supported by a majority of Australian parents and caregivers.
AzVision.az
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