First understand transverse waves,
Transverse waves - A wave in which the medium vibrates at right angles to the direction of its propagation.
Now see non-mechanical waves, non-mechanical waves are electromagnetic waves. These electromagnetic waves have electric field and magnetic field which moves sinusoidally (perpendicular to motion of wave). Since in electromanetic waves, medium vibrates perpendicular to wave, we can say electromagnetic waves are always transverse wave.
Now see mechanical waves, let us say vibration in any body like vibration in string, during vibration particle moves perpendicular to the direction of motion, hence vibration in string is a transverse wave. Thus we can say some mechanical waves like vibration in string are transverse wave.
From above two we can conclude that transverse wave can be either mechanical or non-mechanical wave.