Two pilots and the entire crew were killed. Army Brig. Gen. Domingo Alberto Feneite and Cristian Velazquez, a civilian, were among the victims, according to the state news agency.
Chavez sent condolences to the families of the victims during his weekly television and radio program.
"They died while they were on duty and serving the fatherland," he said.
Neither Chavez nor the Venezuelan military mentioned the cause of the crash.
Chavez lamented that dozens of Venezuelan soldiers have lost their lives in recent years trying during their duties to prevent violence from Colombia's decades-long armed conflict from spilling over into Venezuela.
The socialist leader also rebuked U.S. allegations that his government has failed to prevent border incursions by Colombian rebels and right-wing paramilitaries.
"They say we don't patrol the border. How many lives has Colombia's conflict cost us Venezuelans? Eighteen Venezuelans dead today," Chavez quipped.
The U.S. State Department's annual assessment of terrorism released last week said Venezuela "did not systematically police" the border. It said both Colombian rebels and right-wing paramilitaries "regularly crossed into Venezuelan territory to rest and regroup as well as to extort protection money."
Chavez - a fierce critic of U.S. foreign policy - said he told U.S. President Barack Obama at the recent Americas Summit that he's willing to help broker possible peace talks in Colombia, then added: "It would be great of Obama were to say it, and seek peace instead of fueling the war."
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