Pattinson made the obscene remark during the Sheffield Shield fixture between Victoria and Queensland last week.
His actions were found to be contrary to Cricket Australia's code of conduct - his third disciplinary breach in the past 18 months - due to which he has been ruled out of the first Test.
It has not been confirmed what expletive was used by the paceman but The Australian and the Sydney Daily Telegraph reported it was a homophobic slur.
The 29-year-old, who recently made a comeback to the Test side following a prolonged period of absence, admitted he made a grave error "in the heat of the moment".
"Straight away I realised I was in the wrong, and I apologised immediately, both to the opponent and to the umpires," Pattinson said.
"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."
CA's head of integrity and security Sean Carroll reasoned the sanction imposed on Pattinson was in line with the high standards of behaviour maintained by the board.
"We have a duty to uphold the highest standards of behaviour and the action taken in this matter demonstrates that," Carroll said in a statement.
Australia will not name a replacement for Pattinson in the Test squad.
Pattinson's untimely omission has disappointed Australia skipper Tim Paine, who did not hesitate in condemning the paceman's insolent outburst.
Paine assumed charge as Australia's captain in the aftermath of the ball-tampering scandal in Cape Town last year and has been heralding a change in the team's dressing room culture.
The wicketkeeper-batsman told broadcaster ABC that Pattinson had "let himself down, he's let the group down".
"We actually had a chat last night about the fact that we hold ourselves to a really high standard now with our behaviour," he said.
"That's not just while we're playing (Test) cricket, we've got to go back to domestic cricket and lead the way on that front as well.
"We're disappointed ... but James has owned up and knows he's made a mistake and has apologised for it and will come back bigger and better."