Caracas broke off ties with Bogota in February over its support for opposition leader Juan Guaido in his power struggle with President Nicolas Maduro that has ground to an impasse.
Thursday's deployment in the western state of Tachira was part of an operation being carried out across the country, head of operational strategic command Admiral Remigio Ceballos told reporters from the Tienditas border bridge, which has been closed since February.
"We will continue to carry out operations to fight against drug and fuel traffickers," Ceballos said, adding that 20 tons of drugs had been seized throughout the country.
The current exercises began shortly after a massive blackout in Venezuela on July 22, which Maduro blamed on an "electromagnetic attack" by the United States.
The economically-devastated South American nation is suffering from shortages of food, medicine and other essentials amid the standoff between socialist Maduro and Guaido, who has been recognized as interim president by more than 50 countries including the United States.
After the border was closed, many Venezuelans crossed into Colombia via hidden trails linking the two countries, putting themselves at the mercy of smugglers and armed groups.