Sir Edmund Constantine Henry Phipps KCMG CB was a British diplomat.

Phipps was educated at Harrow School and entered the Diplomatic Service in 1858.

In 1873, he was Third Secretary in Rio de Janeiro and was requested by the Ambassador, George Buckley Mathew, to report on the condition of British emigrants in Brazil.

In 1881, Phipps was promoted from the rank of Second Secretary to be Consul-General at Budapest with the rank of Secretary of Legation, and in 1885 was posted to be Secretary of the Embassy at Vienna. In 1892 he was appointed Secretary of the Embassy at Paris and in the following year promoted to be Minister Plenipotentiary under the Ambassador to France, the Marquess of Dufferin and Ava.

While in Paris, Phipps was a British delegate to an international conference on the prevention of cholera, in 1894. He was made a Companion of the Bath in the Queen's 1894 Birthday Honours. In the same year he was appointed British Ambassador to Brazil.

In 1900 Phipps was appointed Envoy Extraordinary and Minister Plenipotentiary at the Court of His Majesty the King of the Belgians. He was knighted as a Knight Commander of the Order of St Michael and St George (KCMG) in the 1902 Coronation Honours list "for services in connection with the Sugar Conference". This was the Brussels Sugar Convention of 5 March 1902, which was controversial in Britain and was opposed by Henry Campbell-Bannerman amongst others. Phipps retired from the Diplomatic Service in 1906 and died in 1911.

Constantine Phipps was the only son of the Hon. Edmund Phipps, and grandson of Henry Phipps, 1st Earl of Mulgrave. His maternal grandfather was Lieutenant General Sir Colin Campbell. In 1863 he married Maria Miller Mundy, daughter of Edward Miller Mundy, of Shipley Hall, Derbyshire, and his wife Maria Jane, daughter of Rear-Admiral Sir John Hindmarsh; their son Eric became a diplomat in his turn, serving in the 1930s as ambassador successively to Berlin and Paris. Maria Phipps died in 1902, and in 1904 he married Alexandra Wassilewna, widow of Gomez Brandão of Rio de Janeiro, who died in 1954.