Malan, 33, played the last of his 15 Tests in August 2018.
Seamer Saqib Mahmood is included, while spinner Jack Leach misses out but will be on standby as back-up to Moeen Ali.
England fell to a 151-run defeat in the second Test, having drawn the first match in the five-Test series.
The third Test will begin at Headingley in Leeds on Wednesday, 25 August.
Malan has scored 724 runs in Tests at an average of 27.84, including one century and six half-centuries.
“Dawid Malan deserves his opportunity in the Test arena,” said England head coach Chris Silverwood.
“He has a lot of experience across all formats and, if called upon, I am confident that he can come and do well on his home ground.”
Sibley – who averages 28.94 in 22 Tests – has struggled against India this summer, scoring just 57 runs in four innings.
“Dom Sibley needs some time away to regain his confidence after a challenging period,” Silverwood said.
“He will return to Warwickshire to spend time in the middle without the scrutiny and find some rhythm and confidence.
“Dom offers a lot of value to the Test environment and some time away should help him. However, he remains part of our plans.”
Kent batsman Crawley has 15 Test caps and scored 267 against Pakistan in August 2020 but lost his place in the team after the first Test against India and will also now head back to his county.
“Zak is still a massive part of our plans moving forward, but we feel he would benefit from time outside the pressure of international competition to get some time working on his skill,” Silverwood added.
“He has a bright future and I do not doubt that his time will come again in the Test arena.”
England are also hopeful that Mark Wood will be recover from a shoulder injury sustained in the second Test, while Lancashire’s Mahmood could be in line for a Test debut.
“He is confident, highly-skilled and will not be overawed if he is to make his Test debut. His temperament and attitude are suited to the international arena,” Silverwood said of Mahmood.
England squad: Joe Root (capt), Moeen Ali, James Anderson, Jonathan Bairstow, Rory Burns, Jos Buttler (wk), Sam Curran, Haseeb Hameed, Dan Lawrence, Saqib Mahmood, Dawid Malan, Craig Overton, Ollie Pope, Ollie Robinson, Mark Wood
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