Hugo Chavez is in hospital in Cuba after cancer surgery, and has suffered complications caused by a lung infection.
Legislators voted to give Hugo Chavez as much time as he needs to recover.
He has not been seen in public since his last operation a month ago.
Earlier, Vice-President Nicolas Maduro had confirmed that Hugo Chavez would be unable to attend the ceremony.
Venezuela’s opposition has called for the Supreme Court to rule on what should be done if Hugo Chavez is absent.
Its leader, Henrique Capriles, says Hugo Chavez should be declared absent, with the speaker of the National Assembly, Diosdado Cabello, taking over as interim president.
President Hugo Chavez, who has been in power since 1999, was re-elected in October for a fourth term.
The government insists that the inauguration is a mere formality for an incumbent leader.
After weeks of speculation, Diosdado Cabello announced to legislators that Hugo Chavez had requested to be sworn in at a later date before the Supreme Court, according to Article 231 of the Constitution.
“On the recommendation of his medical team, the process of post-operation recuperation will have to be prolonged beyond 10 January, [as a result of which] he will be unable to present himself on this date to the National Assembly,” he said, reading a letter from Vice President Nicolas Maduro.
On Monday, Diosdado Cabello called on Hugo Chavez supporters to take to the streets of Caracas on Thursday to show support for him.
He said several foreign leaders had agreed to be at the Miraflores Presidential Palace on inauguration day.
But Henrique Capriles urged them to stay away and not succumb to “a game by a political party”, meaning Hugo Chavez’s ruling party.
In his most recent update on Hugo Chavez, Information Minister Ernesto Villegas said his condition was “stable”, and he was “responding to the treatment”.
Venezuela’s constitution
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