Manze spent his childhood in Bedford. He went to Bedford School where he learned to play the violin. While studying Classics at Cambridge University he started to play the Baroque violin. Then he studied with Simon Standage at the Royal Academy of Music, and then he studied with Lucy van Dael at The Hague and with Marie Leonhardt.
In 1988 he became first violinist of the Amsterdam Baroque Orchestra which was conducted by Ton Koopman. He also played with two other musicians: the harpsichordist John Toll and the lutenist Nigel North, in a trio called Romanesca.
From 2003 to 2007 he directed The English Concert. He also introduced many music programmes on BBC Radio 3 and appeared in television programmes, e.g. Handel's Water Music. He often performed with the harpsichordist Richard Egarr. He has appeared twice at the BBC Proms.
Manze is now taking a rest from playing the violin and concentrating on conducting. He lives in Sweden where he is Principal Conductor of the Helsingborg Symphony Orchestra and Principal Guest Conductor of the Norwegian Radio Orchestra. He is also Associate Conductor of the BBC Scottish Symphony Orchestra.
In 2011 Andrew Manze was awarded the Rolf Schock Prize laureate in Musical Arts, a Swedish prize which is awarded every three years