He apprenticed in the Holy Roman Empire where he was born in Salzburg, in the Reoublic of Venice, and in the Papal States in Bologna and Rome.
Some time before 1710, Braun came to visit Prague (also in the Holy Roman Empire), already as a full-fledged artist creating from sandstone, and soon he became domestic in Bohemia.
Braun then was able to found the biggest workshop in Prague, employing six journeymen and having an income of 900 golden a year around 1725.
Soon, he himself could not manage the number of new commissions for Prague palaces, gardens, churches and many other places in Bohemia, a situation worsened by the progressing tuberculosis.
Matthias Braun is probably the most famous for his collection of the allegories of Virtues and Vices situated at the Kuks Hospital in Bohemia, a commission of count František Antonín Špork.