- William Andrew Quarles (4 July 1825 28 December 1893), Lawyer, politician, railroad executive, and a general in the Confederate States Army during the American Civil War from Tennessee. Member of Clarksville Lodge No. 89, Clarksville, Tennessee.
- William Howard Quasha (19 May 1912 – 12 May 1996), engineer, lawyer, USA soldier, Boy Scouting official in the Philippines. Grand Master, Grand Lodge, F&AM, Philippines. Chairman, President, CEO, St. Luke’s which named its medical school the St. Luke’s College of Medicine William H. Quasha Memorial. Worked with Rensis Likert on the Revised Minnesota Paper Form Board Test. Known for his 1964 trip to the Vatican to foster amity between Masonry and the Catholic Church.
- Matthew Quay (30 September 1833 – 28 May 1904), United States Senator from Pennsylvania. Member of St. James Lodge No. 457, Beaver, Pennsylvania.
- Manuel L. Quezon, First president of the Commonwealth of the Philippines under U.S. occupation rule in the early period of the 20th century. Raised 17 March 1908 at Sinukuan Lodge No. 272 (renamed Sinukuan Lodge No. 16). First Filipino Grand Master of the Grand Lodge of the Philippine Islands that was established in 1917.
- Henry B. Quinby (10 June 1846 – 8 February 1924), 52nd Governor of New Hampshire. Member of Mount Lebanon Lodge No. 32, Laconia, New Hampshire.
- Josiah Quincy III (4 February 1772 – 1 July 1864). Massachusetts U.S. Representative, Mayor of Boston, and 16th President of Harvard University. Raised in St. John’s Lodge of Boston, 28 March 1795.
- Edgar Quinet (17 February 1803 – 27 March 1875) French historian and intellectual. A Freemason, but his lodge is not known.
- John A. Quitman (1 September 1798 – 17 July 1858), 10th and 16th Governor of Mississippi. Raised in Hiram Lodge No. 18, Delaware, Ohio, in 1820, and affiliated with Harmony Lodge No. 1, Natchez, Mississippi in 1822, serving as master two years later. Was grand master of the Grand Lodge of Mississippi from 1826–37 and 1845-46. He was a 32° Scottish Rite (Southern Jurisdiction) and intimate friend of Albert Pike, who conducted a lodge of sorrow in his memory in 1860. Was an honorary member of the grand lodges of South Carolina and New York.