Chris Dehring is so concerned that he has appealed to fans to seek accommodation early for the March 5 to April 28 event.
"We don't expect to satisfy the entire demand. You can't. It is a tremendous amount of demand for the Cricket World Cup," Dehring told the Barbados Nation newspaper on Wednesday.
"Those who want to attend must appreciate that it is really going to be a challenge. They need to get out there and book their flights and hotel accommodations very early. They should have done so already, but it's not too late."
To help solve the problem, cruise ships may be brought in to cater for the extra supporters.
"The reason there is a fear that there is not enough accommodation is because the demand for the Cricket World Cup in the Caribbean is so exceptionally high," Dehring said.
"The Caribbean is already a destination of choice around the world. It is one of the world's great tourist destinations. Putting the Cricket World Cup in the Caribbean only makes it a destination of unbridled desire."