Soldiers were briefly deployed after the unusual scenes in one of Africa’s most stable democracies.
The president defeated his main rival, former President John Mahama, in December’s tightly fought election.
He faces the twin challenges of dealing with the coronavirus pandemic and trying to boost the economy.
Ghana has had more than 50,000 confirmed cases of the virus, and like many countries has experienced major economic disruption.
Things came to a head in parliament while MPs were voting on a new speaker. The situation escalated after one MP snatched a ballot paper and tried to run out of the building with it.
“There was total breakdown of law and order,” said MP-elect Kwame Twumasi Ampofo of the opposition National Democratic Congress (NDC).
Scuffles between MPs from the NDC and Mr Akufo-Addo’s New Patriotic Party (NPP), neither of which has a majority, were eventually broken up by soldiers who briefly intervened.
An NDC MP, Alban Bagbin, was later sworn in as speaker. It is the first time Ghana has a president and speaker from different parties.
Earlier this week, in what was the final speech of his first term in office, President Akufo-Addo had urged parliamentarians to unite and accommodate each others’ views.
The two parties have exactly the same number of MPs in the newly elected legislature, so there is the possibility of political gridlock.
Last week the NDC filed a petition at the Supreme Court seeking to annul President Nana Akufo-Addo’s victory, citing voting irregularities.
The president obtained 51.6% of the vote in the 7 December election, compared with 47.4% won by Mr Mahama, who served in the top job from 2012 to 2017.