Anselmi was born in Castelfranco Veneto, Treviso. Her father was an assistant pharmacist, and her mother and grandmother ran an inn together.
She attended the local high school, and then the Teaching Institute in Bassano del Grappa. In September 1944, Nazi soldiers forced her and a group of other students to witness the hanging of a group of 31 young Partisans. As a result, she joined the Italian Resistance movement and became part of the Cesare Battisti brigade. That year she also joined the Christian Democracy Party. After World War II, she studied literature at the Catholic University of Milan and became a primary school teacher.
While working as a teacher, Anselmi held positions in Christian trade unions, including the primary teachers' union from 1948-55. In 1959 she joined the national council of the Christian Democracy Party, and she was the party's deputy leader from 1968-92. In 1963, she was elected vice-president of the Female Board of the European Union. From 1958-64 she was head of the Christian Democracy party's youth programmes.
From 1968 to 1987 she was a Member of the Italian Chamber of Deputies, re-elected five times in the Venice-Treviso district. She served three times as undersecretary to the Department of Work and Social Services, and in 1976 she became the first woman to be a member of an Italian cabinet, being chosen by Giulio Andreotti as Minister for Labour and Social Security. She held this position from 1976-79. She served as Minister for Health from 1978 to 1979.
Anselmi is best known for having been the main proposer of Italian laws on equal opportunities, a matter she always fought for in her political life. For example, in 1977 she passed a bill which recognised fathers as primary caregivers for their children, and allowed for both fathers and mothers to have time away from their children. In the same year, a major piece of legislation was passed on gender parity in employment conditions, of which Anselmi was a key supporter. She chaired the National Equal Opportunities Commission until 1994, and played a significant role in the introduction of Italy's National Health Service.
In 1981, she headed the Parliamentary Commission of Inquiry into the illegal P2 Masonic Lodge (Commissione parlamentare d’inchiesta sulla Loggia massonica P2); the lodge, at the time, was considered a threat to society. Anslemi wrote the Commission's final majority report that was approved in 1984, and all activity of the lodge ceased the following year.
Anselmi was the chair of a commission of inquiry into the work of Italian soldiers in Somalia, and of a national commission on the consequences of laws for the Italian Jewish community. She was an honorary vice president of the National Institute for the History of the Liberation Movement in Italy.
Later in her life, she began to write about her experiences in the Resistance; in 2003, she wrote Aunt, what was the Resistance?" ("Zia, cos'è la Resistenza?"), a book explaining the Italian Resistance to young people.
In 2004, she wrote a second book for young people, Bella ciao: la resistenza raccontata ai ragazzi.
In 2006, she published her memoirs, with Anna Vinci, as Story of a Passion for Politics (Storia Di Una Passione Politica).
Anselmi died at home in Castelfranco Veneto, Treviso on 31 October 2016, aged 89.
In 1998, Anselmi was awarded the Knight Grand Cross of the Order of Merit of the Italian Republic.
In June 2016, Anselmi was featured on an Italian postage stamp, the only living person to be honoured in this way.