Venezuela's information ministry said yesterday in a statement that the air force late on Monday "detected and intercepted a Hawker 25 aircraft with the registration XBMGM" in the southwestern state of Apure, near the Colombian border.
The statement quoted the head of Venezuela's strategic command Vladimir Padrino Lopez.
Mexico's foreign ministry said it sent a diplomatic note asking Caracas to "explain the incident in strict adherence with international law."
The air force released pictures of the wrecked plane, with fire still raging in what remained of the fuselage.
Venezuela monitors its border with Colombia to combat drug trafficking. The air force has brought down 13 aircraft linked to drug smuggling this year.