Mushfiqur Rahim had an angry confrontation with a teammate after a collision almost caused a dropped catch in a domestic T20 match.
Nine Bangladesh players resumed individual training at four venues under strict safety measures.
Mushfiqur Rahim tweeted saying he was "hurt" to hear that Shahid Afridi had tested positive for COVID-19.
Former Pakistan captain Shahid Afridi stepped in to buy a bat owned by Bangladesh's Mushfiqur Rahim after a charity auction for coronavirus victims was derailed by fake bids.
Nayeem Hasan claimed five wickets as Bangladesh beat Zimbabwe by an innings and 106 runs in the one-off Test in Dhaka on Tuesday.
Bangladesh ended their innings on 560 for six in the final session before Nayeem Hasan claimed two wickets in two balls in the first over in Dhaka.
Mushfiqur Rahim's absence could be a blow for Bangladesh who are already without suspended all-rounder Shakib Al Hasan.
India vs Bangladesh: Bangladesh fast bowler Al-Amin Hossain said Virat Kohli's dismissal off a stunning catch gave the visiting side some spark to continue the fight.
India vs Bangladesh: Virat Kohli scored his 27th Test century, while Ishant Sharma picked up four wickets to pile misery on Bangladesh.
India vs Bangladesh: Mominul Haque's move to bat after winning the toss backfired as Indian bowlers restricted Bangladesh for 150 in the first inning.