The Scorchers secured their spot in Saturday's decider with a seven-wicket win over the Sydney Sixers in Perth.
A crowd of around 50,000 is set to converge on Optus Stadium for the grand final as the Scorchers attempt to win their fifth title.
Richardson injured his hamstring on January 4 and was initially expected to return in time for the finals.
But the 26-year-old will fall short in his quest to be part of the team's bid for back-to-back titles, with the Scorchers not wanting to put Richardson's body at risk of another injury.
"I think Jhye's chances are pretty slim. I'd be surprised if we see him next weekend," Scorchers captain Ashton Turner said.
"Jhye's such an exciting cricketer, but he's still a young guy.
"He puts his body through a lot. We're really thankful he's done everything he can to get up for the finals campaign. We know how valuable he is.
"But we also have a bit of perspective. Jhye's got a lot of cricket ahead of him - in orange, playing for WA, playing for Australia, playing for franchises around the world.
"He's too important to put unnecessary risk on his body.Â
"We want him in our team as many times as possible. But there's also a risk-reward balance, and I don't think it's worth putting someone's young body under too much stress."
The Scorchers will lose pace ace Lance Morris to international commitments for the decider, with coach Adam Voges facing a tough decision on whether to replace him with fellow paceman Matt Kelly or spinner Peter Hatzoglou.
Kelly missed 'The Qualifier' win over the Sixers through concussion, while Hatzoglou was overlooked altogether after the Scorchers decided to enter the match without a specialist spinner.
"Peter Hatzoglou has bowled really nicely for us over a couple of years now. He was really unfortunate to miss selection," Turner said.
"He's someone who should be playing at this level. He's got a proven track record, he's won us games.
"With Lance missing, there's an opportunity, whether it be for Matt Kelly or Peter Hatzoglou."
Turner was the hero on Saturday night, cracking an unbeaten 84 off 47 balls as the Scorchers recovered from 3-22 to chase down their target of 152 with nine balls to spare.
Cameron Bancroft (53no off 45 balls) was also crucial in the win.
The Sixers are still a chance to reach the grand final, but they will have to beat either the Melbourne Renegades or Brisbane Heat in 'The Challenger' in Sydney next Thursday in order to book their spot.
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