The 28-year-old sustained the injury during Brisbane's match against Melbourne Renegades at the Gabba on Thursday which the home side lost by eight wickets.
Before the start of the BBL, the right-arm bowler had said that his aim is to be able to play in the 2019 Ashes series and join the Australian Test trio Mitchell Starc, Josh Hazelwood and Pat Cummins.
"To not have been available to play in a Test series together so far is a bit disappointing. We always talk about how good it would be to play together, so that's another driving factor, to get up back with them," Pattinson told cricket.com.au.
"You hear the media talk about the 'Big Three' and you think, two years ago it was the 'Big Four'. You think about how good that bond could be if we could get it all together, and we could rotate through Test matches," he added.
Pattinson played a total of five matches in the ongoing season of the BBL with a wicket count of four.
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