The lawyer and MP who swore Odinga in -- TJ Kajwang -- was arrested on Wednesday afternoon and was being investigated for his role in the ceremony, according to a senior police officer speaking on condition of anonymity.
After initially vowing to block the gathering, police kept their distance, but a furore broke out after the Communication Authority shut down three of the country's main private television channels who were covering the ceremony.
"What was witnessed at Uhuru Park was a well-choreographed attempt to subvert or overthrow the legally-constituted government of the Republic of Kenya," Interior Minister Fred Matiangi said in a statement.
"Some elements in the media fraternity participated in furtherance of this illegal act," he charged.
Matiangi said the authorities had information that "criminal elements operating under the banner" of the National Super Alliance (NASA) opposition coalition had planned to "shed blood" at the event and "blame it on the police".
That was why police had withdrawn from the venue, he said.
Matiangi said the outlets -- among them NTV, Citizen TV and KTN -- would remain shut until an investigation was finished.
The Media Council of Kenya said in a statement it was "shocked at the recent turn of events."
"A political contest has turned into the greatest threat and assault on freedom of expression and media in Kenya’s recent history," it said.
The shutdown came after media organisations were summoned to State House last week for a meeting.
During the meeting, Kenyatta, his deputy William Ruto and other senior officials warned editors against live coverage of the ceremony and threatened to revoke their licenses if they failed to comply, according to Linus Kaikai, chairman of the Kenya Editors' Guild.
Rights groups on Wednesday criticised the gagging of the media.
"Kenyan authorities have restricted media coverage at a critical moment, and violated the public's right to information about important events," said Otsieno Namwaya, Africa researcher at Human Rights Watch (HRW).
HRW said the shutdown "underlines a trend since 2013, when Kenyatta took office for the first time" of intimidation, harassment and threats aimed at the media.
"Kenya is on a very slippery trajectory in regard to human rights, and president Kenyatta urgently needs to reverse this trend," Namwaya said.
Matiangi said Odinga's swearing-in itself was also under investigation and that "appropriate legal action" would be taken.
Authorities had repeatedly warned that such an inauguration would be treasonous and that Odinga could face arrest.
However, as the wording of the oath was different to that in the constitution, the consequences of Odinga's act of political theatre remain unclear.
Three of Odinga's co-leaders of NASA failed to show up at the event, including Kalonzo Musyoka who was to be sworn in as his deputy, raising speculation of a rift in the opposition.
Kalonzo said they did not attend after their bodyguards were withdrawn.
Then, on Wednesday he said his home had been attacked in the early hours of the morning, with shots and a stun grenade fired at his house.
Police said they were investigating.
Odinga has refused to accept Kenyatta's victory, which came after last year's deeply-divisive election season in which rights activists say at least 92 people were killed.
First was an election on August 8 that was won by Kenyatta then annulled in a historic decision by the Supreme Court, which ordered a re-run on October 26.
Odinga boycotted the second vote and Kenyatta won with 98 percent.
Since boycotting the re-run poll, citing a lack of reform at the election commission, NASA's strategy has been to challenge Kenyatta's legitimacy by seeking to establish parallel government structures.
Matiangi on Tuesday denounced the opposition's National Resistance Movement wing, tasked with implementing a threatened programme of boycotts and civil disobedience, as an "organised criminal group".
"It is a group of individuals who are bent on causing anarchy and mayhem," he added on Wednesday.
"We will not accept subversion and criminal acts disguised as political activities. This will not be tolerated."