Air force radars "detected the entry to Colombian territory of two Venezuelan military aircraft in the Alta Guajira zone" on the northern border with Venezuela on Saturday afternoon, the ministry said in a statement yesterday.
The planes, it said, entered Colombia for nearly three kilometres and then flew over an army unit.
The ministry did not describe the type of aircraft detected.
Bogota and Caracas have been in a spiralling row since Venezuelan President Nicolas Maduro closed part of their shared border on August 19, blaming Colombian paramilitaries for an attack on a Venezuelan anti-smuggling patrol.
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Venezuela has deported some 1,500 Colombians living in Venezuela since the crisis began, and more than 18,500 others have fled in fear, the United Nations said.
The foreign ministers of Colombia and Venezuela met in Ecuador on Saturday in an attempt to resolve their differences, and while they agreed to renew diplomatic contacts after ambassadors were withdrawn, they failed to agree on a meeting between the two country's presidents.
In 2010, troops were rushed to the border after the Colombian president accused Venezuela of giving safe haven to leftist Colombian guerrillas.