Two windows of the bus were smashed as it was leaving the Sher-e-Bangla stadium after the match in what police claimed was a case of mistaken identity.
"The fans thought it was the Bangladeshi team bus and they hurled stones at it," Imtiaz Ahmed, deputy commissioner of police in Dhaka, told AFP.
"The window panes were shattered, but no one was injured."
West Indian star Chris Gayle, a former national captain, had tweeted from the vehicle during the attack, claiming the players had been terrified.
"This is ridiculous. Damn. World Cup with so much security and this happens.
Big joke. Trust me I am not keen here. Every player lay flat," he wrote on his Twitter account.
He added: "This is some bullshit.....Bangladesh stoning our bus!!! Freaking glass Break!!! This is crap, can't believe..what next, bullets!!!!" Bangladesh Cricket Board president Mustafa Kamal apologised to the West Indies for the incident.
"We are sorry it happened," Kamal told AFP.
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