Raja Sir Tanjore Madhava Rao, KCSI (20 November 1828 – 4 April 1891), also known as Sir Madhava Rao Thanjavurkar or simply as Madhavarao Tanjorkar, was an Indian statesman, civil servant, administrator and politician who served as the Diwan of Travancore from 1857 to 1872, Indore from 1873 to 1875 and Baroda from 1875 to 1882. He was the nephew of the former Diwan of Travancore T. Venkata Rao and the son of T. Ranga Rao who was also the former Diwan of Travancore .

Madhava Rao was born in a prominent Deshastha Brahmin family of Kumbakonam in 1828 and had his education in Madras. After serving for two years in the Madras civil service, Madhava Rao was appointed tutor to the princes of Travancore. Impressed with his performance, Madhava Rao was transferred to the Revenue Department in which he rose step by step to become Diwan in 1857.

Madhava Rao served as Diwan of Travancore from 1857 to 1872 bringing about developments in education, legislation, public works, medicine, vaccination and public health and agriculture. He was also responsible for clearing Travancore's public debts. Madhava Rao quit as Diwan of Travancore and returned to Madras in 1872. He served as Diwan of Indore from 1873 to 1875 and as Diwan of Baroda from 1875 to 1882. In his later life, Madhava Rao actively participated in politics and was one of the early pioneers of the Indian National Congress. Madhava Rao died in 1891 in Mylapore, Madras at the age of 63.

Madhava Rao was respected and regarded for his administrative abilities. British Liberal statesman Henry Fawcett called him "the Turgot of India". In 1866, he was made a Knight Commander of the Order of the Star of India.