Hennessey was born on a farm in Manchester, Iowa, in 1932, the thirteenth child of Maurice Hennessey and Anna Killias. At the time of her birth, her oldest sister Dorothy was already a Franciscan Sister. Their sister Miriam would also leave home and enter a religious institute before Gwen had started school. Their brother, Ronald, later became a Maryknoll priest serving in Latin America.
Hennessey graduated from St. Patrick's High School in Ryan, Iowa, at age sixteen. She then remained at home for the following year to help her mother. It was during this year that her sense of being called to become a Religious Sister became more pronounced and she followed her sister Dorothy in entering the Sisters of the Third Order of St. Francis of the Holy Family, based in Dubuque, Iowa.
Hennessey earned a Bachelor's degree in English literature and education at Briar Cliff College (now Briar Cliff University) in Sioux City, Iowa, which was run by her religious congregation. She took her final religious vows as a member of the congregation on August 10, 1956, following which, she was assigned to teach. Her teaching career would include assignments in both Iowa and Illinois.
While assigned to serve at a school in Chicago, Hennessey became involved with the organization Clergy and Laity Concerned, through which she became active in the nuclear disarmament movement. She also attended the Jesuit School of Theology in Chicago where she studied Liberation theology. Following Chicago, Hennessey helped start the Catholic Peace Ministry in Des Moines, Iowa. She then earned a Master's degree at the Maryknoll School of Theology in Maryknoll, New York. During her period on the East Coast, she became co-Director of the Maura Clarke/Ita Ford Center in Brooklyn, New York, and served with the Appalachian Office of Justice and Peace in southwest Virginia. Eventually she returned to Dubuque, where she and her older sister Dorothy served at Mount St. Francis, the motherhouse of their congregation.
In 1997 Hennessey then became involved in the activity for which she is most widely known, the protests at Fort Benning, Georgia, home of the Army's School of the Americas, a facility for training Latin American soldiers. In 2000, Gwen Hennessey, along with her natural sister, Sister Dorothy Hennessey, O.S.F., were both arrested, and in 2001 they were convicted and sentenced to six months in jail for their protest.
Hennessey believes that the School of the Americas teaches torture techniques to Latin American soldiers, and that graduates of the program have been involved in atrocities, including the 1989 murders of six Jesuit priests and two women in El Salvador. The school denies these claims and argues that it helps to spread democracy in Latin America.
She took part in a protest march in the 1960s in Antioch, Illinois. African Americans were banned from the city, and Martin Luther King, Jr. was marching with her. She also helped Cesar Chavez, leader of the United Farm Workers, organize migrant workers in California.
In 2002, Gwen Hennessey, along with her sister Dorothy Hennessey, was awarded the Pacem in Terris Award. It was named after a 1963 encyclical letter by Pope John XXIII that calls upon all people of good will to secure peace among all nations. Pacem in terris is Latin for 'Peace on Earth'.