Organisers announced the suspension at 11:45 a.m. local time (0045 GMT), some 35 minutes before the leading group were scheduled to tee off.
John Senden and Britain's world number four Justin Rose will be the last players to take to the course with the Australian holding a two-shot lead as he bids for a second title at his home Open.
Eight-times major winner Tom Watson, already well out of contention, was an early starter and scored an impressive three-under-par 69.
The American said the conditions could make the final round a lottery.
"A good score is even par," he said. "It will be interesting to see what happens. It's a really strong wind. Yesterday it blew like hell." (Reporting by Nick Mulvenney, editing by Ian Ransom)