She gained notoriety for slapping a cameraman in 2005 when she stormed the offices of a private media group in anger at the way a story about her had been reported.
In a tribute to Mrs Kibaki, President Uhuru Kenyatta praised her for her role in fighting HIV/Aids in Kenya.
Mr Kenyatta succeeded her husband Mwai Kibaki, who governed from 2002 to 2013.
Mrs Kibaki, who was born in 1940, had withdrawn from public life during the latter part of her husband's rule.
She was last seen at a public function in August  2010, when she seemed excited about the adoption of a new constitution, dancing to a famous gospel song, Kenya's Daily Nation newspaper reports.
Mr Kenyatta said she had been unwell for the last month, receiving treatment in both Kenya and the UK.
Mrs Kibaki trained as a teacher, leaving her job not long after her marriage in 1962 to raise her four children.
"Her Excellency will be remembered for her immense contribution in the development of country," Mr Kenyatta said in a statement.
According to the Daily Nation, she organised the First International Aids Run in 2003.
But correspondents say she also provoked condemnation when she said unmarried young people had "no business" using condoms, calling on students to abstain from sex in order to avoid infection with HIV.
Mrs Kibaki was the most controversial of Kenya's first ladies, crossing swords with politicians, diplomats, journalists and policemen she believed had not treated her with sufficient respect.
Just months after her husband became president, she is reported to have shut down a bar inside State House that was a watering hole for ministers and close allies of Mr Kibaki.
In 2005, she stormed into the house of her neighbour, the World Bank's then-country director Makhtar Diop, in a tracksuit at midnight and demanded he turn his music down at a private party to mark the end of his posting in Kenya.
She also went to the local police station in shorts to demand that Mr Diop and his guests be arrested for disturbing the peace.
Later, she burst into the offices of the influential Nation Media Group with her bodyguards and demanded that the reporter who had written about her confrontation with Mr Diop be arrested.
She slapped cameraman Clifford Derrick who was filming her and refused to leave the offices until 0530 the next day.
He tried to sue for assault, but the case was thrown out of court.
In 2007, Mrs Kibaki was filmed by Nation TV slapping an official during an independence day celebration at State House.
Security officials seized the video images and erased the slapping incident, before returning them.
Kenya's controversial former first lady, Lucy Kibaki, has died in a London hospital of an undisclosed illness.