The third placed Frenchman said he had suffered major damage to the port foil in storm conditions and would have to assess the damage before deciding whether to continue on the round the world race.
Race organisers said on their website that worsening weather was expected in the area 600 nautical miles off the Australian coast.
A statement said Josse "has temporarily put the race to one side and is currently studying the best possible options to allow the worst of the storm to go by."
Meanwhile race leader Armel Le Cléac'h is setting a record pace, arriving off Australia more than five days ahead of the previous best time.
The skipper of Banque Populaire VIII took 28 days 20 hours and 12 minutes to cross the imaginary line off the southern Australian cape of Leeuwin. He cut five and a half days off the previous best time set in 2012 by fellow Frenchman François Gabart.
For the run from Cape of Good Hope to Australia Le Cléac'h took just 10 days and 16 hours.
With almost half the race gone, Le Cléac'h is 13,460 nautical miles from home and leads second-placed Briton Alex Thomson, sailing Hugo Boss, by 107.7 miles.
"It's nice to be in the lead at the second cape. Alex was in the lead at Cape of Good Hope and I am in the lead at Cape Leeuwin. So much the better," he said on the race website.
