In one wing of the opera house, off to the left of the main entrance, is the Museo Teatrale alla Scala (Theater Museum of La Scala).
The first photo shows the entrance to the museum, which is also the entrance to the galleries when there is an opera performance. And this is also where the scalpers tend to hang out trying to sell black-market tickets at exorbitant prices.
The museum consists of ten rooms with displays of musical instruments, paintings and other artifacts from the history of opera in general and La Scala in particular.
Also there is a space for temporary exhibitions. When I was there the exhibit was on the singer Maria Callas at La Scala.
At that time, no photography was allowed inside the museum. (Now they allow photos for private use, with no flash.)
The museum is open almost every day (all except nine days per year) from 9 am to 12.30 pm (last entrance at 12 noon) and from 1.30 pm to 5.30 pm (last entrance at 5 pm). A normal full-price admission ticket costs nine Euros (as of 2018) and includes a glimpse of the auditorium from one of the boxes, except when rehearsals or performances are in progress.
When I was there they were adjusting the lighting for the first act of Verdi’s Macbeth (as in other opera houses, an extra player wearing one of the costumes had to stand around for hours while they did this), but we were allowed to have a look just the same.

Trailer with Malibran exhibition
For three days during my visit to Milan there was a large trailer from the Cecilia Bartoli Music Foundation parked outside the museum. In it was an interesting free exhibition on the singer Maria Malibran (1808-1836). Malibran was the big star of La Scala for three seasons in the 1830s. Of course Cecilia Bartoli herself was also in town to give a recital of arias from Malibran’s repertoire, “Malibran Rediscovered”.
http://www.teatroallascala.org/en/
My photos in this post are from 2008. I revised the text in 2018.