Francis Lewis Shaw Merewether (18 March 1811 – 27 December 1899) was an English-born Australian politician. Merewether served as the Chancellor of the University of Sydney between 1862 and 1865.
He was the son of clergyman Francis Merewether and Frances Elizabeth Way, and attended Eton College and Cambridge University. In 1838 he migrated to Sydney, where he worked in the treasury department and as an immigration agent. In 1841 he married Kate Amelia Plunkett, with whom he had five children. He was a non-elective member of the New South Wales Legislative Council from 1851 to 1856, during which time he served as Postmaster-General (1851–52) and Auditor-General (1852–56), as well as acting Colonial Treasurer (1854–56). He served in the re-constituted Council from 1856 to 1861 and from 1861 to 1865, when he retired. Merewether died in Essex in 1899.