That will depend. If you need the same correction for both eyes and you have no eye problems with non-prescription reading glasses, then they won't harm your eyes. If your non-prescription reading glasses cause eye strain or headache, then you need prescription glasses.
Non prescription reading glasses are made with the same power in both lenses. They are suitable for people whose eyes have the same power in both eyes. However, most people have different unique prescription. If you have your own unique prescription, non prescription reading glasses will make you feel uncomfortable and actually cause problems instead of helping to correct vision. Some people will even have sore eyes and dizziness when they wear non prescription reading glasses for a long time. So it is better and more saft to wear prescription one.