Prime Minister Anthony Albanese and NSW Premier Chris Minns are among those to have paid tribute to her, with the latter reflecting on her advocacy for mental health, education and social inclusion.
A psychiatrist and the wife of former Sydney lord mayor Nicholas Shehadie, Dame Marie served as NSW governor from 2001 to 2014.
"On behalf of the people of NSW, I extend my deepest condolences to Dame Marie's family, friends and all those who were inspired by her remarkable life," Mr Minns said in a statement late on Tuesday.
"The people of NSW held Dame Marie in great respect and affection, reflecting the trust and goodwill she earned over a lifetime of service."
Dame Marie was born to a Lebanese father and a mother of Lebanese descent in Narrandera in southwestern NSW, and worked at two Sydney hospitals before taking up general practice as she commenced her medical career.
She then studied psychiatry and worked in senior positions within NSW Health before her ascent to governor.
She was appointed an officer of the Order of Australia in 1988 for her services to child and adolescent health.
Dame Marie said she didn't extend her tenure as governor so as not to surpass Roden Cutler as the state's longest-serving governor, a decision Mr Minns said "reflected her humility and deep respect for those who came before her".
""Dame Marie Bashir served our state with distinction as the first female Governor of NSW from 2001 to 2014, bringing to the role immense dignity and compassion," Mr Minns said.
The prime minister said Australia was poorer for death and richer for her life due to her dignity, warmth, intellect and empathy.
"Her lifetime of service to the medical profession, her community and her fellow Australians was defined by her powerful sense of duty and her abiding passion for helping others," Mr Albanese posted on Twitter.
"As the first woman to serve as Governor of NSW she was both a pioneer and an inspiration."
NSW state MP Alex Greenwich honoured her support for the LGBTQI community, which included her and her husband being named chiefs at the 2015 Sydney Gay and Lesbian Mardi Gras for their work to combat homophobia.
"Throughout her career she always supported the rights and equality of the LGBTIQA+ community from the AIDS crisis to the marriage equality campaign," he wrote on Facebook.
A state funeral is to be held at a later date.
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