Born in Lund, the son of the theologian Lorenz Murbeck, superintendent in Karlskrona, Muhrbeck was first taught by a tutor and then attended school in Karlskrona.
After his return to Sweden he became a teacher at the cadet institute in Karlskrona.
Muhrbeck, who published numerous philosophical writings, was a staunch supporter of Christian Wolff and a staunch opponent of Immanuel Kant.
His son Friedrich Philipp Albert Muhrbeck later also taught philosophy in Greifswald, but was a follower of Kant and Johann Gottlieb Fichte.
The daughter Ingeborg Juliane Elisabeth Muhrbeck (1784-1824) married the lawyer and historian Karl Schildener in 1803.