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.
Bangladesh Cricket Board president Mustafa Kamal apologised to the West Indies for the incident.
"We are sorry it happened," Kamal told AFP. "We have already ordered an investigation and the police are working on it.
"There was enough security for the buses, the fans may have thought it was the Bangladesh bus. The stones were thrown from a long distance.
"It is nothing serious. No serious damage was done, but still we are very sorry this happened."
Violence also broke out in the Dhaka University campus as angry students torched Bangladeshi team jerseys and placards after the home team's comprehensive defeat, a top police official said.
West Indies spokesman Philip Spooner, whose team were playing in Bangladesh for the first time since 2002, confirmed there were no injuries.
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