To compound those killings, six prisoners transferred from Uribana after the violence were shot and stabbed to death on being moved to a new prison.
"It is the result of failings in internal security and infrastructure," Chavez told state television.
Chacon will be replaced by Pedro Carreno, a Chavez loyalist who heads a parliamentary judicial commission and who played a leading role in the president's re-election campaign last month.
Chavez gave no reason for removing Rangel, who has often been one of the toughest advocates of the president's self-styled leftist revolution.
"The decision to relieve Jose Vicente of his post was not easy for me because he is like a star pitcher and I regard him with the same respect and affection as a son would a father," Chavez said.
Rangel will be replaced by Jorge Rodriguez, a Chavez ally who served as a director of the country's electoral commission during a heated recall referendum against the president in 2004.
Rodriguez, a psychiatrist, is idolised by many of Chavez's followers because of his father, who died after being tortured by the army for alleged involvement with a left-wing guerrillas in the 1970s.