No. The changing electric and magnetic fields are the wave. A electric and magnetic field can change without a medium, although until semi-recently many scientists thought that a medium was required for a wave to propagate. They hypothesized an all pervasive static medium called the aether. The Earth and all heavenly bodies traveled through it.

In the late 19th century the michael-morley experiment showed that there wasn't a static aether. It determined that light travels at the same speed in perpendicular directions. If light was propagating through a stationary aether then the light would have taken different times to travel one way vs its perpendicular since the Earth, the galaxy, and everything else is moving.

Relativity further poke a hole in the bottom of the boat for an aether since it doesn't accept a static absolute reference frame for anything. And a medium would not support everyone everywhere agreeing that the speed of light is the same.