Francis Burke may refer to:
- Francis Burke (Franciscan) (died 1697), Irish Franciscan friar and writer
- Francis Burke (bishop) (died 1723), Irish Roman Catholic archbishop of Tuam
- Francis Burke (Dean of Elphin) (1834–1904), priest of the Church of Ireland
- Francis Michael Burke (1876–1949), Australian politician
- John Francis Burke (1923–2006), Canadian politician
- Joseph Francis Burke (1914–1980), American arranger, composer, band leader and producer
- Maurice Francis Burke (1845–1923), Irish-born prelate
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