Finch - generally considered a specialist one-day batsman - has been hailed as being in "sensational form" by national selector Trevor Hohns.
He is joined in a 15-man squad by Michael Neser, Brendan Doggett, Mamus Labuschange and Travis Head.
Finch, 31, has spent the summer with Surrey while also impressing in national colours, beating his own world-record score with 172 in a T20I against Zimbabwe in July.
This series, to be played in the UAE, represents Australia's first Test action since the ball-tampering scandal which engulfed their spring tour of South Africa.
Former captain Steve Smith, opener David Warner and Cameron Bancroft are unavailable for selection as a result of their suspensions owing to that incident, while pace duo Pat Cummins and Josh Hazlewood are injured.
"There has been significant change to our Test squad, due to the unavailability of a number of key players," Hohns said.
"That said, we firmly believe the squad selected is up to the challenge ahead, and is capable of playing a brand of cricket that can perform well in this series against Pakistan."
Tim Paine captains the side, while Peter Siddle - enjoying a strong summer with Essex - returns having played the last of his 62 Tests in November 2016.
If Doggett gets the call, the 24-year-old would become the second indigenous cricketer to play a Test match for Australia, following Jason Gillespie.
Justin Langer will coach Australia for the first time in Tests, with the first match starting in Dubai on October 7.
Australia squad: Tim Paine, Ashton Agar, Brendan Doggett, Aaron Finch, Travis Head, Jon Holland, Usman Khawaja, Marnus Labuschange, Nathan Lyon, Mitchell Marsh, Shaun Marsh, Michael Neser, Matthew Renshaw, Peter Siddle, Mitchell Starc.
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