Alonso had jinked his McLaren to the left of Haas' Esteban Gutierrez as they slowed to take a corner but his car clipped the rear of Gutierrez's vehicle and the front left wheel of the Spanish driver's car was ripped off.
The McLaren pitched against an outside wall at top speed before rolling through the gravel and coming to rest against a far wall in one of the most horrific-looking accidents at Albert Park.
Alonso was given the all-clear by doctors. He somehow managed to walk away from the mangled wreckage and hoards of debris unharmed.
He and Gutierrez were taken to the medical centre for assessment.
The team later confirmed via Twitter he had been "formally okayed by the doctors".
"I'm sure his marbles are rattled a little bit," McLaren chief Ron Dennis told Sky Sports.
Stewards will investigate the incident. The accident triggered a red flag, bringing proceedings to a temporary halt.
Alonso missed the 2015 Australian Grand Prix following a crash during testing in Spain. He joined Gutierrez, Daniil Kvyat (Red Bull), Rio Haryanto (Manor) and Kimi Raikkonen in retiring from the season-opening GP.
The race began with pole-sitter and reigning world champion Hamilton botching the start. Hamilton slipped from first to sixth in the blink of an eye as Ferrari's Vettel sped into the lead at the first turn.
From then, Vettel opened up an advantage of more than 11 seconds over the Mercedes ace only for the forced restart to create a logjam in the field - and make tyre choice paramount. Vettel lost top-billing on his soft tyres as Rosberg and Hamilton drove on medium compound tyres for greater durability - and Rosberg soon assumed the lead.
Ricciardo was second for a stint before being overtaken by Hamilton, the Australian then being forced to pit and change his soft tyres, dropping to fifth. He then produced a late charge but couldn't reel in Vettel while Williams' Felipe Massa came fifth, followed by Haas' Romain Grosjean. AAP