Parkinson, who plays for Lancashire, had been withdrawn from the England Lions tour of the UAE after scans showed up a stress fracture and he has not recovered enough to take up his Stars deal.
Plunkett is a key member of England's white-ball sides and will share overseas duties with Nepal legspinner Sandeep Lamichhane. The Stars have also signed Dwayne Bravo for the duration of the tournament.
Plunkett's next international commitment is likely to be England's one-day series against West Indies which starts on February 20. There is a warm-up match scheduled for February 18, the day after the BBL final, so depending on how far the Stars progress in the tournament his availability could be restricted in the closing stages.
Melbourne Stars squad Michael Beer, Jackson Bird, Scott Boland, Liam Bowe, Dwayne Bravo, Jackson Coleman, Travis Dean, Ben Dunk, Seb Gotch, Evan Gulbis, Peter Handscomb, Sandeep Lamichhane, Nic Maddinson, Glenn Maxwell, Jonathan Merlo, Liam Plunkett, Marcus Stoinis, Daniel Worrall, Adam Zampa