Do you use displacement on the model or its material? Does the model have turbosmooth modifier which may have different settings for viewport and for render? More info please.
If the rest of the map is flat this could be just wrong gamma - make sure your displacement/bump is loaded with 1.0 gamma, not automatic (or 2.2).
Looks like the material was the problem. It was fixed when I turned off the bump map. Thank you for your suggestion.