Fifteen people were rescued, six of whom were minors, the navy told AFP.
The boat sank near the Colombian resort islands of San Andres and Providencia, east of Nicaragua.
Military officials said a search and rescue operation involving navy rapid response units and the air force was underway.
The adults saved were from Colombia, Ecuador, Iran, Nicaragua, Kazakhstan and Venezuela, the navy added.
Of the minors that were saved, two were from Kazakhstan and three from Venezuela. The nationality of the sixth was not disclosed.
In May, Washington imposed sanctions on Nicaragua, accusing it of aiding the trafficking of undocumented migrants seeking to make it to the United States.
Colombia has said that migrants are increasingly using a clandestine route between San Andres and Nicaragua to avoid the dangerous crossing through the Darien jungle between Colombia and Panama, heading north through Central America and eventually to Mexico and the U.S. border.
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