Skrimshire is a surname. Notable people with the surname include:
Baroness Skrimshire of Quarter (1913–1979), Scottish politician Fenwick Skrimshire (1774–1855), English naturalist and physician who certified John Clare as mad Reg Skrimshire (1878–1930), Welsh rugby player William Skrimshire (1766–1829), English surgeon and botanist
See also Scrimshaw (surname)