Batter Ollie Pope, who led England during the home series against Sri Lanka, will lead the tourists in the match, which starts on Monday.
"I tried my hardest to get myself fit for this game, but have taken the call to miss this one because I've not quite managed to get game-ready," Stokes told BBC Sport.
"There is a lot that has to go into my rehab program. We got to a certain point, but looking at the picture of what we've got coming up and physically where I'm at, I'm not quite ready to play.
"It's always frustrating to miss out. I've got some good things to focus on, so even though I'm not playing I've got a goal in mind."
The 33-year-old trained mostly alone before batting in the nets on Saturday before ruling himself out of the first of the three Tests England will play in Pakistan.
Stokes was not sure if he would play the second Test, also in Multan, starting on October 15.
"I've pushed myself incredibly hard and worked really hard with the medical team to get to where I'm at now," he said.
"I think I'm further ahead than what we expected. I'll be working just as hard over the next 10 days to try to get myself fit for the second Test."
England announced their playing XI, which includes Durham seamer Brydon Carse, who will be making his Test debut.
Left-arm spinner Jack Leach makes a return to the Test set-up for the first time since the India tour in January, while opener Zak Crawley rejoins the team after fully recovering from a broken finger sustained during the summer.
Fresh from their 2-1 victory at home against Sri Lanka, England will be favourites in the three-match contest against a Pakistan side smarting from a 2-0 whitewash by Bangladesh last month.
England batter Joe Root, however, would not take any thing for granted.
"We know how good Pakistan is as a team and the ability and skill level they have. You've got to have full respect for that," Root told a press conference.
"In their own conditions, in particular, they've got a number of players that are match-winners and that are capable of doing very special things in Test cricket."
ENGLAND XI: Zak Crawley, Ben Duckett, Ollie Pope (captain), Joe Root, Harry Brook, Jamie Smith, Chris Woakes, Gus Atkinson, Brydon Carse, Jack Leach, Shoaib Bashir
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