Organisers pulled the plug barely half an hour before the 13-lap dash was due to start at a soaking Phillip Island, with winds of up to 80 kilometres (50 miles) per hour forecast.
"Changes were made to the schedule to try and ensure the maximum track action in the safest possible conditions on Sunday," organisers said.
"But the weather conditions – forecast to worsen throughout the day – have obliged the cancellation of further track activity."
Spain's Martin had won the last four sprints and was the pole-sitter for Australia, desperate to claw back points after finishing fifth in Saturday's grand prix to Bagnaia's second.
Bagnaia, the Italian Ducati rider, will now take a 27-point lead over Pramac's Martin into next week's Thailand MotoGP with just four legs of the 20-stop season remaining.
"For me, it's a lost occasion when we lose a race ... I was prepared to fight for the top position and I was positive," said Bagnaia.
"But the wind was quite crazy and with MotoGP riders at 330kph it can become very dangerous, so for me the decision is the correct one."
Six-time world champion Marc Marquez agreed it was the only sensible move.
"In warm-up it was acceptable, but then it looks like the wind was super strong and especially with these bikes, with all aerodynamics we have, it becomes a bit dangerous," said the Spanish Honda star.
Forecast gale-force winds had already seen organisers move the main grand prix forward a day to Saturday to ensure that race took place.
Martin's teammate Johann Zarco won with a last-lap overtake to clock his first victory in 120 starts.
Racing did go ahead at Phillip Island on Sunday despite the bleak conditions, but several riders came to grief on the slippery track in the Moto2 and Moto3 races before the sprint was cancelled.
The writing was on the wall after a chaotic Moto2 race was halted due to high winds with just nine of 23 laps completed.
Italy's Tony Arbolino was declared the winner and half-points were awarded to keep his title hopes alive, 56 points behind Spain's Pedro Acosta who came ninth.
Earlier, Turkey's Deniz Oncu snatched victory from Ayumu Sasaki on the final turns of the Moto3 race to prevent the Japanese rider from grabbing the world championship lead.
Sasaki is now four points behind Spain's Jaume Masia, who came eighth.
