The building dates from the 16th century. It was built to remember the church that had to be demolished for the city walls.

From wikipedia:
"When in 1513 the basilica of San Pier Maggiore was destroyed to make way for the new city walls, only a pylon with an effigy of the Madonna depicted on it remained standing in the old church. When a worker attempted to demolish the pylon, a large flame hit him, mortifying him. The situation was reported to Bishop Sisto Gara Franciotti della Rovere, he decided to leave the pylon untouched by building around it what is now the oratory of the Madonnina."
it.wikipedia.org/wiki/Oratorio_della_Madonnina