Richardson suffered the hamstring injury during the warm-up prior to Australia's T20I loss to Sri Lanka on Saturday and scans have since revealed the extent of the injury.
The right-armer will fly back to Australia and skipper Aaron Finch said the veteran is expected to be sidelined for up to six weeks.
Richardson becomes the fourth Australian player to suffer injury.
Mitchell Starc suffered injury to his finger, while Shawn Abbet and experienced all-rounder Mitch Marsh (calf) also sustained injuries.
Strong Australian team for tomorrow’s match
The Australian team has been named for the first match of the ODI series against Sri Lanka.
The team will be captained by Aaron Finch and will include David Warner, Steven Smith, Marnus Labuschagne, Marcus Stoinis, Glenn Maxwell and Ashton Ager.
Alex Carey will be the wicket keeper while Pat Cummins, Jhye Richardson and Josh Hazlewood will function as fast bowlers.
The five-match ODI series between Sri Lanka and Australia begins tomorrow (14). The first match will be played at 2.30 pm tomorrow at the Pallekele International Cricket Stadium.