Henry Fisher Menzies (15 June 1867 in London, Ontario, Canada – 31 July 1938 in Edinburgh) was a Scotland international rugby union player. Born in Canada to a Greenock father, he moved to Scotland with his mother as a child and was brought up in Perthshire. Educated at Fettes College in Edinburgh, he went on to be a teacher.
After studying at Fettes College, he played rugby for Fettesian-Lorettonians.
He went to Edinburgh University and then played for their rugby team. He graduated in 1889.
He then played for West of Scotland.
He played for Glasgow District in the 1891 inter-city match against Edinburgh District on 5 December of that year.
He played for Cities District against Anglo-Scots on 24 December 1892.
He played for West of Scotland District against East of Scotland District on 21 January 1893.
Henry played four times for Scotland.
His debut was on 4 February 1893 against Wales.
He was appointed a Master at Aberdeen Grammar School. It was in Aberdeen that he married his wife, Margaret Crombie, on 12 August 1896.
Menzies moved from Aberdeen to become a Rector of Wallace Hall academy in Dumfries-shire. He was there for over 30 years until he retired.