The figure of the European explorer, after whom Colombia is named, was dragged from its plinth with ropes and vandalised.
The demonstration marked two months since the start of a nationwide protest movement calling for social reform.
Indigenous activists see Columbus as a symbol of colonialism and oppression.
The mayor of Barranquilla said those responsible would be brought to justice.
The Columbus statue is the latest to be pulled from its pedestal as part of the anti-government protests which have been sweeping through the country.