The nun, who spent most of her life in India, came sixth in the list which was topped by the only female UK prime minister.
Margaret Thatcher beat the Queen and the first female Nobel Prize winner, Marie Curie, to the title.
More than 2,000 adults had their say in the poll for Scottish Widows.
Over a quarter (28%) of people said Ms Thatcher was more influential than scientist Marie Curie (24%) and the Queen, Britain's longest serving monarch, (18%), in an Opinium poll.
Diana, Princess of Wales (17%), suffragette leader Emmeline Pankhurst (16%), Catholic missionary Mother Teresa (13%), nursing pioneer Florence Nightingale (12%), Queen Victoria (8%), African-American civil rights activist Rosa Parks (7%) and broadcaster Oprah Winfrey (6%) also made the top 10.
Aviation trailblazer Amelia Earhart was named the most influential sportswoman, author Jane Austen topped the creative arts list, and actress Judi Dench was named the most influential female performing artist.
Body Shop founder Anita Roddick was named the most influential businesswoman, Simone de Beauvoir the most influential female public intellectual and Kate Adie the most influential female journalist, according to the poll.
Suzannah Lipscomb, historian and author, said: "The top 10 are an impressive list of women. Each of them was or has been responsible for or overseen real change, but in addition nearly every one of them has some symbolic importance beyond their own person.
"What's evident overall is that the women chosen as the top of each category - and in our list of top 10 - are not flashes in the pan.
"Thatcher, Pankhurst, Curie, Earhart, Austen, Dench, Beauvoir and Adie are women who can be referred to by one name. They have been chosen because they were and are game-changers. This is the definition of 'influential' that emerges."
Jackie Leiper, retirement expert at Scottish Widows, said: "The survey results reflect the changing face of women in the workforce since Scottish Widows was established 200 years ago, and the increase of opportunities that have opened up to women to enact genuine influence on society since then."
Mother Teresa was beatified - when the Catholic Church recognise that a person enters Heaven - by Pope John Paul II in 2003, after the first healing miracle was found soon after her death.
Before sainthood a second healing miracle is needed.