Antony was recuperating in the Army Research and Referral Hospital here after a prostate surgery last month and joined office only yesterday.
"The Defence Minister drove down to the Vietnamese Embassy here and paid homage on behalf of the nation to Gen Vo Nguyen Giap, the brilliant commander who brought victory for Vietnam in many wars. Gen Giap passed away in Hanoi on October 4 at the age of 102," a Defence Ministry release said.
Offering the deepest condolences, Antony said India shares the grief of the people of Vietnam on the passing of one of their most respected national heroes.
"Gen Giap's leadership of Vietnam's national liberation had evoked the admiration of the Indian people. He shall remain an inspiration to people all over the world," he said.
He was the longest serving Defence Minister of Vietnam who faced most of the incursions and invasions on the Vietnamese territory as head of the military.