The 26-year-old left-armer, who replaced the injured Zafar Ansari in the squad, has represented England at Twenty20 and one-day level.
England are 3-0 down in the series heading into the fifth and final match of the series.
Pace bowler James Anderson has been ruled out though general soreness from England's fourth-Test defeat in Mumbai.
After Cyclone Vardah recently passed through Chennai, the ground staff at the MA Chidambaram Stadium have dried the wicket using trays of hot coals.
England are likely to opt for a three-spinner attack with Dawson, Moeen Ali and Adil Rashid supplemented by Joe Root's part-time off-spin.
Hampshire's Dawson took three wickets in England's Twenty20 win over Sri Lanka in July and two in the one-day defeat by Pakistan in Cardiff in September - his only two international appearances.
England's leading wicket-taker had been out since August with a shoulder injury before returning to play the second Test of the five-match series in India.
"It's a tough one. He is body sore from the Test match and we don't think he is worth the risk in this situation," said England captain Alastair Cook.
Anderson has taken just four wickets in his three Tests in the series in India.
Cook added: "If it was 1-1, we would probably take that risk but history over the last six months or so has shown us that, when he has played in these situations, injuries have happened.
"We need to look after him. He has got a big part to play for England cricket over the next 18 months or so. He is disappointed but I think it is the right call."
Fellow bowler Stuart Broad has missed the past two Tests with a tendon strain in his right foot and a decision on his fitness will be taken after practice on Thursday.
"Broady is fit and has a chance. He bowled at a local ground on Wednesday. It's great to have him back," said Cook.
England, having drawn the first Test, are 3-0 down in the series going into the final match.
Cook, who said he had "questions" about his role as England Test captain after the fourth match was lost by an innings and 36 runs, will meet with director of cricket Andrew Strauss in January to discuss his position.
"It's a natural thing that happens with me and Straussy now," 31-year-old Cook told BBC Test Match Special. "Often my future comes up and how we want to move forward.
"This would be no different to any of those other meetings and we are going to have to discuss what is the best thing for English cricket.
"You have to be very careful about decisions that are made in the heat of the moment that have a long-term effect on yourself and the team."
Cook, who captained England in Bangladesh in 2010 before taking on the role permanently in 2012, has won 24 of his 58 Tests in charge.
He has also overseen 21 Test defeats, including a 5-0 Ashes whitewash in Australia in January 2014 and England's first Test loss to Bangladesh in October this year.
Cook added: "We've tried to knock it [the issue] on the head as many times as we can, but of course when you lose games of cricket it gets blown up."
Cook believes Joe Root, 25, is "ready to captain England" and his India counterpart Virat Kohli says the batsman is "equipped enough to handle that job".
Kohli has flourished since becoming India captain in 2014 and has won 13 of his 21 Tests and leapfrogged Root into second place in the Test match batting rankings.
"Joe is an outstanding player," said the India captain. "I've been very fond of his game and the way he goes about things. He is very positive, always thinks of any situation as an opportunity.
"I don't know what captaincy would do to that. Captaincy is not just about handling 10 more guys, or having a squad and interacting with the management.
"It comes with the whole package of interacting with the media, having people expect things from you in a very different way, having the onus of the whole country on your shoulders as far as the sport is concerned.
"Joe looks like a guy who has got the temperament to do it but you can only tell well he gets into the scheme of things and how he reacts to it."
India are top of the ICC Test rankings after five series wins in a row and are unbeaten in 17 matches in the longer format of the game.
They have beaten England, New Zealand and South Africa at home, while winning in West Indies and Sri Lanka.
"We still understand we have got a lot of cricket to play around the world," said Kohli. "It's not only about this one period we are going through.
"It looks really good because we have come out of transition and immediately started winning games but I wouldn't take it as a thing for over-confidence.
"It's an on-going process which needs to be sustained for the next seven, eight years for us to become a top-quality side and leave a mark on world cricket, maybe become known as one of the best teams to have been assembled.
"We want to do it across formats and make that mark for Indian cricket on the world stage.
"We don't feel invincible to be honest. We respect every opposition."
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Spinner Liam Dawson is set to make his Test debut for England in Friday's dead rubber against India in Chennai.