This article is from the Formula One Motor Racing FAQ, by firstname.lastname@example.org (Mitchell McCann) with numerous contributions by others.
Perhaps, one of the most annoying frequently asked questions.
Don't ask it in rasf1 unless you want to start a long, tedious
thread. The official answer is its to stop any potential health
hazards to the mechanics from the microwave transmitter which is
housed in the mirror. This transmitter sends telemetry data back
to the pits while the car is on the track. Several "news"
programmes and publications have reported claims that
microwaves, as used in cellular phones can cause cancer etc. etc.
While people more knowledgeable than me claim that this is
impossible, it remains the official explanation as to why they
put the box over the mirror when the mechanics are working around