A strong enough magnetic field can damage just about anything - but computers, CRTs, and DVD players don’t create fields like that if they’re behaving properly.
A burned CD-R or DVD-/+R is susceptible to a fairly common type of radiation though - infrared, or heat, radiation. Intense heat (>120ºF) can cause the dye of burned CDs and DVDs to break down relatively quickly. That’s the only sensible cause I can think of to explain how a DVD that sits on top of the DVD player would be damaged by radiation. So, feel the top of your DVD player with your hand. If you can’t rest your hand there comfortably, you’ll want to keep DVDs and CDs off of it and see if there’s something you can do to improve ventilation around the player.
It’s always a good idea to keep CDs and DVDs away from heat and sunlight. And if you happen to notice metal objects flying across the room towards your appliances, you might have a magnetic field problem…