Events from the year 1864 in Scotland.

• 21 June – last public execution in Edinburgh – George Bryce, the Ratho murderer.^[1]
• 19 July – Chalmers Hospital opened in Banff, Aberdeenshire.^[2]
• 2 September – the first Ottoman ironclad Osmaniye is launched by Robert Napier and Sons on the River Clyde.
• 8 December – James Clerk Maxwell presents his paper A Dynamical Theory of the Electromagnetic Field to the Royal Society, treating light as an electromagnetic wave.^[3]
• Hall, Russell & Company established as marine engineers in Aberdeen.
• The National Bank of Scotland becomes the first Scottish bank to open an office in London.^[4]
• Historian John Hill Burton publishes The Scot Abroad.

• 2 January – James Caird, shipowner (died 1954 in England)
• 17 January – David Torrence, film actor (died 1951)
• 5 February – Marion Gilchrist, medical doctor (died 1952)
• 6 February – John Henry Mackay, anarchist writer (died 1933 in Germany)
• 14 February – James Burns, shipowner (died 1919)
• 8 March – James Craig Annan, photographer (died 1946)
• 28 May – Jessie Newbery, née Rowat, embroiderer (died 1948 in England)
• 10 June – Ninian Comper, Gothic Revival architect (died 1960 in England)
• 1 October – Alexander Grant, biscuit manufacturer (died 1937)
• 7 October – Harrington Mann, painter (died 1937 in the United States)
• 31 October – Cosmo Gordon Lang, Archbishop of Canterbury (died 1945 in England)
• 4 November – Robert Lorimer, architect (died 1929)^[5]
• 13 December – John Quinton Pringle, painter (died 1925)

• 6 January – John Clements Wickham, explorer, naval officer, magistrate and administrator (born 1798)
• 1 June – Sir John Watson Gordon, portrait painter (born 1788)
• 6 August – Catherine Sinclair, novelist and children's writer (born 1800)
• 1 October – Ignatius Spencer, English priest (born 1799)

• Timeline of Scottish history
• 1864 in Ireland