There were no other changes to Australia's 13-man squad in a short statement issued by the team on Tuesday.
Opener Weatherald was out for 23 and 0 in Australia's stunning nine-wicket loss to Bangladesh in Darwin, bringing his average to 20.36 in six tests dating back to his Ashes debut.
Queensland's Renshaw played the last of his 14 tests over three years ago against India in Delhi but has revived his test career after a strong domestic season, having scored 499 runs in six Sheffield Shield matches at an average of 49.90.
While Weatherald is out, number three Marnus Labuschagne's place appears safe for now despite being under plenty of scrutiny after making a total of 32 runs in Darwin.
Head coach and selector Andrew McDonald said on Monday Labuschagne needed "big runs" to shore up his place in the test setup.
Australia will look to level the two-test series against Bangladesh with victory in Mackay, Queensland from Saturday.
Australia squad:
Pat Cummins (c), Scott Boland, Alex Carey, Cameron Green, Josh Hazlewood, Travis Head, Josh Inglis, Marnus Labuschagne, Nathan Lyon, Matt Renshaw, Steve Smith, Mitchell Starc, Beau Webster