Mr Chavez's congressional allies, who hold a majority of seats in the National Assembly, agreed with a government proposal for Mr Chavez to be sworn in at a later date before the Supreme Court.
While pro-Chavez politicians approved the plan, opponents condemned the action as illegal.
Vice President Nicolas Maduro broke the news that Mr Chavez would not be able to attend today's scheduled inauguration in a letter to National Assembly President Diosdado Cabello, confirming suspicions that Mr Chavez's battle with cancer and a related respiratory infection would keep him in a Cuban hospital.
Mr Maduro said Mr Chavez was invoking a provision in the constitution allowing him to be sworn in at a "later date".
The opposition disputed that argument and appealed to the Organisation of American States.
Tensions between the government and opposition have been building for days in the dispute over whether the ailing president's swearing-in can legally be postponed. The president underwent his fourth cancer-related surgery in Cuba last month.
Opposition leader Henrique Capriles has said Mr Chavez's current term constitutionally ends today and the Supreme Court should rule in the matter.
Other opposition leaders have argued the inauguration cannot legally be put off, saying the National Assembly president should take over as interim president if Mr Chavez has not returned from Cuba on inauguration day.