The trial, the first-of-its-kind in the region, involved a small-sized drone, which can carry two passengers for up to 35km
Pattinson was vying with Mitchell Starc for the third pace-bowling spot in the Australia side for the opening match in the two-test series, which starts in Brisbane on Thursday.
The 29-year-old had already been found guilty of two breaches of Cricket Australia's Code of Conduct over the last year and was handed the ban when he admitted abusing a Queensland player during the domestic match last week.
"I made a mistake in the heat of the moment," Pattinson said in a Cricket Australia statement.
"Straight away I realised I was in the wrong, and I apologised immediately, both to the opponent and to the umpires.
"I have done the wrong thing and accept the penalty. I'm gutted to miss a test match, but the standards are there for a reason and the fault is mine."
Cricket Australia said Pattinson would not be replaced in the squad for the two tests against Pakistan, which means Starc is likely to play alongside Pat Cummins and Josh Hazlewood in Australia's pace attack for the match at the Gabba.
Australia have cracked down on bad behaviour by their players since the ball-tampering scandal during a test against South Africa in early 2018 led to one-year bans for then captain Steve Smith and vice-captain David Warner.
"(James) knows that he's let himself down, he's let the group down," Australia captain Tim Paine told ABC Radio on Sunday.
"We actually had a chat last night about how we hold ourselves to really high standards now with our behaviour.
"That's not just when we're playing (international) cricket, we've got to go back to domestic cricket and lead the way on that front as well.
"We're disappointed in that but James has owned up, knows he's made a mistake and apologised for it, and he'll come back bigger and better."
The trial, the first-of-its-kind in the region, involved a small-sized drone, which can carry two passengers for up to 35km
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