Looking at computer monitors will not harm your eyes. Often, when using a computer for long periods of time, just as when reading or doing other close work, you blink less often than normal. This reduced rate of blinking makes your eyes dry, which may lead to the feeling of eyestrain or fatigue.
Try to take regular breaks to look up or across the room. Looking at objects farther away often relieves the feeling of strain on your eyes. Keep the monitor between 18 to 24 inches from your face and at a slight downward angle. Also consider the use of artificial tears. If your vision blurs or your eyes tire easily, you should have your eyes examined by an ophthalmologist.