Several passages of a speech Mr Buhari made on 8 September overlapped with President Obama’s address after winning election in 2008.
His office admitted the sentences were “too close to be passed as coincidence”.
The two men are due to meet at the UN General Assembly next week.
“There was a mistake by an overzealous staff and we regret that this has happened,” Mr Buhari’s spokesman Garba Shehu wrote on Twitter, saying those responsible would be punished.
“President Buhari urges Nigerians to look beyond this incident and focus on the message of change which the country needs in order to restore our cherished value systems.”
Buhari: “We must resist the temptation to fall back on the same partisanship, pettiness and immaturity that have poisoned our country for so long.”
Obama: “Let us resist the temptation to fall back on the same partisanship and pettiness and immaturity that has poisoned our politics for so long.”
Mr Buhari used the copied extracts in launching a campaign called “Change Begins With Me”, part of a bid to tackle corruption in Nigeria.
The irony was not lost to some online, who mocked Mr Buhari.
On the BBC Africa Facebook page though, others were more sympathetic.
“So what’s the big deal? Famous lines from great people are used over and over again by others,” wrote one commentator.
“The message conveyed is the most important thing.”
Earlier this year Melania Trump, the wife of Republican presidential candidate Donald Trump, was accused of plagiarising portions of Michelle Obama’s 2008 Democratic National Convention speech. -BBC