Alberto Bachelet was a military adviser to socialist president, Salvador Allende, who was toppled by Pinochet in a coup in 1973.
He died of a heart attack at the age of 50 after enduring six months in captivity during which he tortured.
Accompanied by her mother, Angela Jeria, Michelle Bachelet visited the mausoleum and laid flowers where her father is buried.
The suffering of the Bachelet family won her sympathy in a country still scarred by the 17 year dictatorship of Pinochet.
First female President
Ms Bachelet claimed a convincing poll win in January which has made her Chile’s first female President.
A doctor and a single mother, she was seen as an unusual candidate in a country considered one of the most socially conservative in South America.
The 54 year old smiled broadly and waved after taking her oath in the coastal city of Valparasio.
Bolivian President Evo Morales, Venezuelan President Hugo Chavez and US Secretary of State, Condoleezza Rice, were among those attending the ceremony.
More than two dozen heads of state were also there.
At the ceremony, Ms Rice offered congratulations to Ms Bachelet who takes over from former President, Ricardo Lagos.
He has urged Chileans to support their new leader, calling her a symbol of a society which has changed for the better toward liberty, pluralism and equality.
Her government extends the rule of the centre-left coalition that has governed Chile since the fall of Pinochet’s military regime in 1990.
Ms Bachelet was jailed and tortured by Chile’s former military junta but is looking to the future with a promise to build a more equitable and tolerant society.
“It will be the government of the citizens,” Ms Bachelet told a crowd of thousands gathered in the square outside the presidential palace on Saturday.
“We do not want to repeat the same errors of the past,” she said, referring to the 17-year dictatorship of Pinochet.
“I am the repository of all the history that had dark and bitter moments but has known how to recover,” she said.
After the inauguration Ms Bachelet drove through the streets of Valparaiso standing in an open car, waving at crowds gathered on the sidewalks, before returning to the capital Santiago.