Metals & Non-metals can undergo displacement reactions.

The given statement is True.

A displacement reaction is a chemical reaction in which a more reactive element displaces a less reactive element from its compound. Both metals and non-metals take part in displacement reactions. 

For example, 
2K(s)+2H₂O_​(aq)⟶2KOH₍aq)+H₂(g) 

In the above reaction, K(Potassium) is a metal which is displacing H(Hydrogen) (non-metal).

Hence, metal and non-metal can undergo displacement reactions.