It is located at the corner of Mathæusgade and Valdemarsgade and was completed in 1880 to design by city architect Ludvig Fenger.

When a law in 1868 finally relinquished ownership of the fortifications and lifted the restrictions in the area immediately outside them, new residential districts sprang up outside the four former city gates which had been dismantled in 1868–69.

This was also the case with Vesterbro outside the former Western City Gate which developed into a crowded and poor working-class neighbourhood.

Like many other Danish buildings of its time, St. Matthew's Church is inspired by North Italian Romanesque brick architecture.

The altarpiece is a mural painted directly on the wall behind the altar by Henrik Olrik depicting the Sermon on the Mount.