Authorities discovered four bodies washed ashore on Curacao, and they say 28 people are missing.
Two men who were believed to have been on the boat managed to swim to shore and were arrested.
An opposition lawmaker in Venezuela's Falcon state, Luis Stefanelli, says about 30 people were on the boat and that they were all younger than 35. He says several minors were among them. Stefanelli says each passenger paid a human trafficker about $100 each.
Curacao is only about 70 kilometers (44 miles) from Venezuela. The Dutch island is a popular destination for Venezuelans looking to escape food shortages, economic disaster, and an oppressive political climate.
Venezuelan President Nicolas Maduro imposed an air and sea embargo on Curacao, Aruba, and Bonaire last week. He alleges food and other goods are being smuggled out of Venezuela to the islands, aggravating shortages.