Richard Salwey (1615 – 1685?) was an English politician who sat in the House of Commons variously between 1645 and 1659. He was a republican in politics and fought on the Parliamentary side in the English Civil War.
Salwey was a supporter of Oliver Cromwell, but broke with him at the end of the Rump Parliament, together with Francis Allen. He was a member of Barebone's Parliament, nominated for Worcestershire. He clashed with Cromwell in April 1653; and he lost his Navy position at the end of the year in a general Admiralty change. He was appointed to the new Council of State formed after the Rump was dissolved, but boycotted its meetings.
From 1654 he was out of the country as English ambassador in Constantinople.
In 1659 Salwey was active again in parliament as a member of the restored Rump parliament. He became a member of committee of the Committee of Safety and Council of State, in May of that year, and a commissioner for the Navy. The Committee sent him with Sir Henry Vane as heads of a delegation to John Lawson, a refractory republican Vice-Admiral, without success. On 16 January 1660 he with William Sydenham was expelled from Parliament; he was sent to the Tower of London.
After the Restoration he was suspected of complicity in the Farnley Wood Plot, in 1663-4.