The event, which the president said was a normal workday, included music and art performances, a 21-gun salute, a military flyover and a National Guard parade.
The Umkhonto Wesizwe (MK) party, formed by former president Jacob Zuma six months ago, said party officials would not take part in the “ludicrous” inauguration ceremony.
The Democratic Party, which won 15% of the vote and 58 seats, also boycotted the first meeting of the National Assembly last Friday.
Mr Ramaphosa retained the presidency despite the ANC's vote falling 17 percentage points and losing 70 seats in parliament.
He did this through power-sharing agreements with his historic rival, the pro-business District Attorney's Office, and other political parties.
The ANC won 40% of the vote, with the DA in second place with 22%.
The coalition is a move to the political center as the ANC's left-wing and populist breakaway parties rejected an invitation to join a national coalition government.
Mr Ramaphosa is expected to appoint a cabinet soon after taking office, which will include his new coalition partner the DA and three other smaller parties. These coalitions hold 68% of the seats in parliament.
The president is also expected to present an agenda to revive the slumping economy.
Under his rule, economic performance continued to deteriorate due to power outages, increased crime, and unemployment.
Mr Ramaphosa first became president in 2018 when his predecessor, Mr Zuma, resigned amid corruption allegations, which he denied.
