Hegseth described the people struck in a post on the platform X as "four male narco-terrorists".
The attack, he said, was carried out on the orders of US President Donald Trump in international waters off the coast of Venezuela.
Hegseth said the boat was carrying a "substantial amounts of narcotics" and was en route to the United States.
He warned that further strikes would follow as long as drugs continued to be supplied to the US population.
This was the fourth deadly strike on boats in the Caribbean that the administration says were laden with drugs.
The previous strikes in September killed a total of 17 people.
After the latest attack, the number stands at 21.
The strikes have drawn criticism, in part because the administration initially provided no explanation of the legal basis for the operations, which critics say amount to extrajudicial killings in international waters.
US media reported on Thursday that the administration viewed the United States as being engaged in a "non-national armed conflict" with drug cartels.
Outlets including the New York Times and ABC News cited a confidential memo outlining the White House's legal rationale, which was circulated to several congressional committees.
According to the reports, the administration classifies the drug cartels and the alleged smugglers associated with them as "unlawful combatants".
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