Stokes – paid a record $2.16 million to play the eight-week IPL season – was instrumental to Pune reaching the knockout phase after a brilliant debut campaign in the cash-rich Twenty20 competition.
The 25-year-old left-handed batsman and right-handed pace bowler scored 316 runs in 12 matches, with a highest of 103 not out, and took 12 wickets.
He is not the only England star who will be missing from the final week's action.
Table-topping Mumbai Indians have also lost Jos Buttler to preparations for the England-South Africa series, which doesn't begin until May 24, three days after Sunday's IPL final in Hyderabad.
Their early departures saw an angry response from former England captain Kevin Pietersen, who blasted the England and Wales Cricket Board.
"I think it's pathetic. An absolute shambles," Pietersen said on Sky Sports on Sunday.
"Stokes should be playing in the semi-final and the final. The last week of the IPL is a huge occasion."
The England duo will join the rest of the squad for an ECB training camp in Spain this week.
"What are they going to Spain for?" said Pietersen. "To field a couple of balls? He should be playing in the IPL.
"Just speak to him, speak to Jos Buttler, they'll talk about how much it has helped their development being out there."
Supergiant skipper Steve Smith said other players would have to step up Stokes's absence.
"We have a couple of options (to replace) Stokes," said Smith, who is also the Australia captain.
"He has been magnificent and will be a big loss. Hopefully, the other guys will stand up for us."
Supergiant thrashed Kings XI Punjab by nine wickets in their final regular season match on Sunday to take second spot behind Mumbai.
They meet in the first qualifying playoff in Mumbai on Tuesday, with the winners going straight into Sunday's final.
The losers get another crack at reaching the final on Friday against the winners of Sunrisers Hyderabad and Kolkata Knight Riders, who will clash in Wednesday's eliminator playoff in Bangalore with the losers heading home.
The Rohit Sharma-led Mumbai have been the outstanding side in this year's IPL, with 10 wins from their 14 matches and will enjoy home advantage at the Wankhede Stadium for the first playoff encounter against Pune on Tuesday.
Australia vice-captain David Warner leads third-placed finishers Hyderabad while veteran Indian opener Gautam Gambhir leads fourth-placed Kolkata as the 10th season of IPL cricket heads for Sunday's finish line.