Richardson will replace injured quick Josh Hazlewood (side strain) but Warner has been deemed fit to play in the day-night Test at Adelaide Oval starting Thursday.
Warner has barely batted after being struck in the ribs during Australia's nine-wicket win over England in the series-opener in Brisbane.
But Australia's captain Pat Cummins says Warner won't miss the second Test.
"He will be right," Cummins told reporters on Wednesday.
"He had a bat yesterday and batted in a bit of discomfort ... but he'll be fine.
"It's not an injury like a broken bone ... (but) he might be in a bit of discomfort.
"If he thought he couldn't be as good as he normally is, he wouldn't be playing."
Cummins said Warner was not expected to have a pain-killing injection before playing.
"It's an option if he needs it but I think he will go out and bat and see how it goes," he said.
Paceman Richardson will play his first Test match since February 2019, winning selection as Hazlewood's replacement ahead of Michael Neser.
Cummins rated Richardson, a 25-year-old who has played two Tests, as in the "upper echelon" of fast bowlers.
"He swings the ball both ways, he's a bit faster than you think ... and he's really consistent," Cummins said of the West Australian.
"He's more than ready to go."
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