The incident took place while the president's helicopter was flying through Colombia's Catatumbo region toward the city of Cucuta, capital of the country's Norte de Santander province, Duque said.
"What's clear is that this is a cowardly attack where bullet holes can be seen in the presidential aircraft," Duque said.
As well as Duque, the helicopter was carrying other officials including Defense Minister Diego Molano, Interior Minister Daniel Palacios, and governor of Norte de Santander Silvano Serrano.
No one was injured in the incident, a spokesman for the presidency said.
Security personnel have been given clear instructions to find those behind the attack on the helicopter, the president added.