In a statement issued on Wednesday, the interior ministry also said that it would keep three independent TV stations, which had planned to broadcast the event, off air pending investigation.
They said that broadcasting the event amounted to a "serious breach of security".
Citizen, NTV and KTN TV were taken off the air by authorities on Tuesday over plans to cover the ceremony at Nairobi's Uhuru Park.
Also on Wednesday, local media reported that an opposition politician who had presided over the swearing-in had been arrested.
TJ Kajwang was said to have been taken to the headquarters of the Directorate of Criminal Investigations in Nairobi.
Odinga took an unofficial oath as the 'people's president' on Tuesday. The ceremony took place three months after he boycotted a presidential election rerun.
"Today's step is one step towards the doing away with electoral autocracy and to establishing proper democracy in our country," the leader of the opposition coalition, NASA, said after taking his oath.
Kenya's Attorney General, Githu Muigai, had said in December that Odinga's alternative swearing-in ceremony would amount to treason.
Reporting from Nairobi, Al Jazeera's Catherine Soi called the interior ministry's statement "very tough".
"It's going to be interesting to see how these investigations will conclude and whether it will lead to the arrest or Raila Odinga," she said.
"It's also going to be problematic to arrest him," she continued.
"He has a huge following as you can see from the number of people, the thousands upon thousands who showed up to witness the ceremony on a work day ... But government officials are saying that nobody is above the law."
Odinga, 72, refused to take part in an election rerun in October, claiming the government planned to rig the vote.
President Uhuru Kenyatta won a second and final five-year term in office and was sworn in as president in November.
The East African country's Supreme Court annulled August's presidential election result saying the electoral commission committed "irregularities and illegalities" during the vote, harming the integrity of the election.
Kenyatta, the son of the country's founding father, had also won August's vote.