Does a semiconductor follow Ohm's law?
Yes. All materials under normal conditions and at fixed temperature follow* ohm's law, though it becomes less useful in good insulators where breakdown occurs before any substantial amount of current can flow.

Non-ohmic effects occur at boundaries between different materials, such as pn junctions, schottky junctions, thermocouples, electrochemical cells, et cetera. They can also be observed in discharge phenomena, where the flow of current causes ionization and chemical changes in the conducting material.

*Here, "follow" means "behave in a way closely approximated by". Depending on how precisely you're measuring things, it may matter that it's not quite exact.

Edit: it's worth mentioning that the presence of (changing) magnetic fields can complicate things. Transformers and inductors are not generally considered to obey ohm's law under dynamic conditions, for instance.

For further information on where it gets murky, see this question.