He reached the third round at last year’s Australian Open, but will fall further down the next set of rankings after this qualifying failure.
He was left out in 2015 after accusing the governing body of abandoning him following hip surgery in 2014, but has since returned to the team.
Further questions were raised about his attitude when he held his racquet by the strings when facing match point in a Madrid Open tie last year.
“I just count money, that’s all I do,” he told Channel 7.
It will be the first time since 2008 that 25-year-old Tomic has not featured in the main draw, with Tennis Australia having chosen not to offer the world number 142 a wildcard.