If sound passes through material, vibration is produced. So are electromagnetic waves produced too?

A sound wave passing through a medium (e.g. air) indeed displaces molecules by a distance of a few nanometers. It seems reasonable that it should also displace the atoms, and thus electrons and protons in the process, which are charged particles and should radiate by Larmor's equation when undergoing acceleration.

Let us assume the sound frequency is on the order of kHz (which is in our audible range). Then molecules are accelerated by

$$a \approx \left(10^3\, \mathrm{Hz}\right)^2\times \left(10^{-9}\, \mathrm{m}\right) \approx 10^{-3}\, \mathrm{m/s}^2 $$

Then the predicted power of the radiation produced by Larmor's equation is ridiculously small $$P = \frac{2}{3}\frac{q^2 a^3}{c^3} \sim 10^{-73}\, \mathrm{W} $$ Even if one multiplies this by the number of molecules of air in a $\mathrm{m}^3$, $N\approx 10^{25}$, this would never be detectable. Therefore, this effect may well exist, but it is absolutely negligible in all respects.

N.b. My answer focused on direct effects of the acceleration of air molecules due to a sound wave. As other answers mention correctly, there are interesting secondary effects of (especially large-amplitude) sound waves involving EM radiation. Among these are sonoluminescence and heating of the air by sound dissipation leading to increased thermal radiation.

If it passes through a piezoelectric material, it may generate a measurable voltage and current, some fraction of which will be radiated. For most materials, however, there won't be a detectable effect.

Physically vibrating atoms with a sound wave will technically accelerate the charges, but the radiation emitted will be very weak. However secondary effects from the sound wave are a different matter.

Indeed, sound waves in water can create light. This is called sonoluminescence. In the lab it's done with ultrasound passed through cavitation bubbles. It also happens naturally, with the pressure waves created by the rapid motion of the mantis shrimp's claw.

The exact mechanism is as yet unknown. One hypothesis is that the physical shock from the sound wave ionizes the particles of dissolved gases, which recombine and emit light.