Is an artificial neural network a kind of metaheuristic? In a research paper i have written i am solving a problem through the use of an ANN, which learns to model a technical process through training data.

I compare that to metaheuristic approaches, which can also find relevant outputs from inputs by searching, e.g., with a genetic algorithm and an appropriate cost function.

A reviewer gave me the feedback that ANN are also a kind of metaheuristics, so i should not compare ANN vs. metaheuristics as different kinds of approaches in the paper. Is this correct? I have looked up the definition of metaheuristic and while i think that i could use a metaheuristic optimizer instead of a gradient based one, an ANN itself is not a metaheuristic.
I suppose one could possibly argue it either way, but at the end of the day, it doesn't really matter whether we classify an ANN as a metaheuristic.  It sounds like you have one reader who found it off-putting or confusing to have you compare ANN vs metaheuristic because they would have characterized an ANN as a metaheuristic.  So, I suggest asking yourself three questions: (1) How many other readers will have a similar reaction?  (2) What changes can I make to the paper that would avoid that reaction?  (3) Is there any downside to those changes?  Are they worth it?

In this case, it seems easy enough to rephrase your description of the comparison, so you don't trigger this reaction.  You could be more specific about what comparison you are doing: you compare an ANN to a genetic algorithm.  That might avoid the problem, with no downside.  Being specific is often a good thing.