The former military Head of State could not attend because of prevailing health issues.
Babangida was the Head of State who infamously annulled the June 12, 1993 presidential election that was presumably won by Abiola in what is described as Nigeria's freest and fairest election. After Abiola refused to give up his mandate, he was imprisoned in 1994 by another military leader, Sani Abacha, and died in custody under suspicious circumstances on July 7, 1998, four years after his arrest.
Explaining his reason for missing the ceremony on Tuesday, it was announced that the former military leader was absent "because of some prevailing issues that particularly touches on his health".
Babangida has been questioned for years for his significant role in the annulment of the election that set Nigeria's democratic development back for a few more years.
During an interview on Channels Television on Sunday, June 10, 2018, Tundun, Abiola's daughter, said Babangida has already privately apologised to Abiola's family for his role in the controversial event.
She said, "Regarding IBB, he has actually apologised to the family. IBB has said in public, but stopped short of apologising in public, that his life was threatened. He was afraid for his life.
"He was told by certain factors that, 'Abiola must never become Commander-in-Chief of this country. We will kill him and we will kill you'. So, he was afraid; he has actually admitted to that publicly. He did not want to die, so he annulled the election."
When asked why she thinks Babangida has not publicly apologised for his role in the annulment, Tundun said he must be finding it hard to humble himself.
"Ego. It's difficult to humble yourself. A whole IBB, the evil genius, Maradona, to be sort of remorseful. Even for him to publicly admit fear with all of that legend around his person must have been difficult for him to do. He regrets it," she said.
Another notable absence from the ceremony is former president, Olusegun Obasanjo, who said he couldn't attend because he's away in Norway.
While the president was speaking on Tuesday, he apologised to the family of the late Abiola, on behalf of the federal government, for his death in the struggle to hold on to his mandate.
Buhari said, "On behalf of the federal government, I tender the nation's apology to the family of late MKO Abiola who got the highest votes and to those that lost their loved ones in the course of June 12 struggle."
The president asked everyone in the Conference Hall to stand for a one-minute silence in honour of MKO Abiola and all those who lost their lives in the aftermaths of the annulled election.