She was born Siobhán Giollamhuire Nic Cionnaith in Belfast in the newly created Northern Ireland into a Catholic and nationalist family.

Her father Eoghan McKenna (born Millstreet, County Cork, 1892) was Professor of Mathematics at University College, Galway (UCG).

[3] She is remembered for her English language performances at the Abbey Theatre in Dublin where she would eventually star in what many consider her finest role in the George Bernard Shaw play, Saint Joan.

[7] She received a second Tony Best Actress nomination for her role in the 1958 play, The Rope Dancers, in which she starred with Art Carney and Joan Blondell.

In 1979 McKenna appeared in the title role of Roald Dahl's "The Landlady", an episode of the British TV series Tales of The Unexpected.