Venezuelan Foreign Minister Elias Jaua
"It is the mandate that comandante President Hugo Chavez gave us," Jaua said late on Tuesday.
He did not explain if the election would be held within a month or if the date for the election would be announced during this period.
Earlier in the day, Chavez died after a nearly two-year battle with cancer.
"We have just received the most tragic and awful information. At 4:25 p.m. (2055 GMT) today March the 5th, President Hugo Chavez died," a tearful Maduro said, directly from a Caracas military hospital.
On February 18, the 58-year-old Venezuelan leader returned to Caracas from Cuba, where he had cancer surgery.
Chavez traveled to Havana on December 10 for a fourth operation after his cancer reappeared, despite a year and a half of treatment.
In late March 2012, Chavez began radiation treatment in Cuba after an operation in February 2012 that removed a second cancerous tumor from his pelvic region. Chavez’s first tumor, which was baseball-sized, was removed in June 2011, and then he received chemotherapy.
Chavez, who came to power in 1999, was reelected to a new six-year term in October.