Anne or Anna Molson was born on April 8, 1824, in Montreal, Quebec, daughter of William Molson (1793–1875) and Elizabeth Badgley Molson (1799–1887).

She was a philanthropist, born into a family that was at the forefront of many major economic and technological changes in Canada, and was involved in the industry, banking, philanthropy, education, and politics. She played a major role in breaking the gender barrier at McGill University. Anne wanted to study physics and mathematics when she was young, but McGill University didn't admit women at the time. She was determined that her own daughter Edith would have the opportunity to do so. Her association with McGill began in 1864 when she arranged to donate an annual medal for honourable achievement in science, physics, and mathematics - the Anne Molson Gold Medal. Together with Margaret Dawson, they founded the Montreal Ladies' Educational Association in 1870, Anne being elected its first president. McGill University opened the first class for women in 1871. She was also involved in various Montreal charities, including the Montreal Ladies’ Benevolent Society and the “Maternity,” and she was an honorary president of the Montreal Society of Decorative Art.

In 1845, she married her cousin John Molson (1820-1907). She died on January 3, 1899, in Atlantic City, New Jersey, and is buried in Montreal, Quebec.