Mr Chavez said a lesion he had removed from his pelvic region earlier this week was malignant.
In a televised messaged recorded in Cuba, where he is being treated, Mr Chavez said the tumour had not spread.
The news comes just seven months before presidential elections in Venezuela, in which Mr Chavez has promised to run for re-election.
In the footage, recorded in Havana on Saturday and broadcast on Venezuelan TV on Sunday, Mr Chavez said his recovery had been progressive and rapid.
He said tests showed the tumour was "a recurrence of the initially diagnosed cancer", but stressed that "the tumour was totally extracted''.
The president said he would undergo radiotherapy, but did not say whether he would do so in Cuba or in Venezuela.
Smiling and walking
Last year, Mr Chavez had surgery and four rounds of chemotherapy in Cuba after a baseball-sized growth was detected in his pelvic region.
Since the latest round of surgery, Mr Chavez has been upbeat, using the Twitter social network to tell officials and supporters he would "live and win".
In pictures released on Friday, he could be seen smiling broadly and walking unaided. And in a phone call to Venezuelan television, he thanked the "love from the people".
He has not said when he will return to Venezuela.
"I cannot neglect my recuperation treatment for even a minute,'' he said on Friday.
"I continue recovering, thanks to Venezuela's support, the Cuban people, the doctors here in Cuba, to the love from the people that fills me," he added.
Venezuelan President Hugo Chavez says he has had a recurrence of the cancer he was treated for last year.