Ivan Duku was approaching an airport near the border with Venezuela on Friday when his plane was hit.
Photos published later showed bullet holes in the rotor and tail of the helicopter.
No one was injured in the attack.
The United Nations, the European Union and the United States have condemned the attack.
Defense Minister Diego Molano, who was also on the plane, offered a reward for all the information that leads to the culprits.
National police, meanwhile, said they found two rifles they say were used in the attack.
The 7.62 caliber rifle had “Venezuelan Armed Forces insignia”, said the head of the national police.
“We are looking for those responsible. We will not give up until we catch them,” he said.
It is not yet known who carried out the attack.
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