The piece has been created by artist Bill Viola as a companion piece to his Martyrs (Earth, Air, Fire, Water) work, unveiled at the London church in 2014.
The video triptych features Mary with Christ on her knee in one scene, while another shows a woman breastfeeding.
Viola has exhibited other "works for sacred spaces" at Durham Cathedral and Saint Mark's Basilica in Milan, Italy.
"Mary is a universal female figure present in nearly all spiritual and religious traditions," said the US artist.
"She is the personification of the feminine principle, related to ideas of creativity, procreation, inner strength, love and compassion."
The Reverend Canon Mark Oakley, chancellor of the cathedral, called the work "a contemporary contribution to a long tradition of reflection on the life and significance of Mary".
The triptych, he continued, "encompasses the great themes of birth, relationship and death which is our shared experience of being human."
Mary can be seen, free of charge, in specially escorted timed sessions held between 11:30 and 14:15 on every day except Sunday.
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A large-scale video installation based on the Virgin Mary has gone on display in St Paul's Cathedral.