During his speech, a man grabbed the microphone before dragged away, after which Mr Maduro criticised security and said he could have been shot.
Thousands gathered on the streets of Caracas to show their support for Mr Maduro and to celebrate independence.
The ceremony follows a decision to audit votes cast in Sunday’s election.
Mr Maduro was elected president ahead of opposition leader Henrique Capriles by 1.5% of the vote.
Mr Capriles, who believed there were voting irregularities, says he accepts the electoral audit.
Opposition supporters were expected to protest against Mr Maduro’s inauguration by banging on pots and pans, and playing salsa music.
Dozens of leaders from across the region (including Brazil, Cuba and Colombia), Iran and some Arab countries attended the ceremony.
Mr Capriles made an appeal for peaceful protests in a bid to avoid further violence after clashes left seven people dead on Monday.
The National Electoral Council’s decision to audit all the paper receipts of electronic votes is seen as a major concession to the opposition.
The council had earlier audited 54% of the vote and said this showed that Mr Maduro, the chosen successor of the late President Hugo Chavez, had won a slim majority.
The official count indicates Mr Maduro won 50.8% of votes to Mr Capriles’s 49.0%.
Mr Capriles said he believed the crucial votes that cost him the presidency are among the unaudited 46% of the vote.
He said there were more than 3,000 incidents from Sunday’s poll that needed to be examined.
Correspondents say the announcement comes as a surprise to many after the electoral body initially said the the results, which it announced on Sunday night, were “irreversible”.
The council’s president, Tibisay Lucena, told AFP news agency that the expanded audit was not a recount but would cover all ballot boxes not audited on election day by reviewing a sample two-thirds of them over the next month.
Venezuela uses electronic voting machines which register an elector’s decision and then emit a printed receipt for the voter to deposit into a sealed ballot box. For the audit, the receipts will be compared with the electronic tallies, to check for any irregularities.
Russian President Vladimir Putin and Cuban leader Raul Castro were among the first heads of state to congratulate Mr Maduro on his win.
The governments of Brazil, Peru, Ecuador, Colombia, Bolivia and Argentina, among others, have also voiced their backing for Mr Maduro’s victory.
But the US has so far refused to recognise Mr Maduro’s win, calling for an audit of the results.
Secretary of State John Kerry said the US was not yet ready to validate the results of Sunday’s poll.
Several opposition-led protests erupted across the country after the official results were announced on Sunday