| Office: | Senator |
| Term Start: | 22 July 1954 |
| Term End: | 22 May 1957 |
| Constituency: | Nominated by the Taoiseach |
| Term Start1: | 14 August 1951 |
| Term End1: | 22 July 1954 |
| Term Start2: | 8 September 1943 |
| Term End2: | 18 August 1944 |
| Constituency2: | Industrial and Commercial Panel |
| Birth Date: | 4 April 1894 |
| Birth Place: | County Galway, Ireland |
| Party: | Independent |
| Spouse: | Deirdre O'Donnell |
| Children: | 2 |
Frank J. Hugh O'Donnell (4 April 1894 – 4 November 1976) was an Irish critic, playwright and politician.
O'Donnell was born at Shop Street, Tuam, County Galway to John O'Donnell and his wife Delia (née Carr) but spent his childhood in Milltown, County Galway. O'Donnell was enrolled in Milltown National School in November 1902 aged eight and left in June 1909 aged fifteen. He and his brother Patrick O'Donnell worked in the family business in Tuam before moving to Dublin to work in the clothing industry. He was a published critic of music, literature and theatrical performances, and wrote a weekly letter in the Gael, a weekly paper. He was also a playwright, having some of his works staged at the Abbey Theatre.
His first play The Dawn Mist (1919) follows a Galway family, the Egans, who lose two brothers and an uncle in the 1916 Easter Rising. The play became very popular, however; it was banned by the British authorise earning the title of "Ireland's most proclaimed [banned] play".
In 1943 he became a member of Seanad Éireann on the Industrial and Commercial Panel where he promoted Irish arts and culture.[1] He lost his seat at the 1944 Seanad election, but was re-elected at the 1951 election. He was nominated by the Taoiseach to the Seanad in 1954.
O'Donnell had two children, with his second wife, Deirdre.
A collection of O'Donnell's papers and manuscripts dating from 1911 to 1974 kept at the University of Delaware Library, is open for research.
He bore almost the same name as a contemporary politician, Frank Hugh O'Donnell, also from County Galway.