Is it normal that my baby doesn't want to play with toys or other objects?

Yes. It depends on your baby's age. In the first month, babies are not interested in toys. After that, they become more visually interested, say in looking at a pattern or a mobile. By 3-4 months, anything that can be grabbed and chewed on is a toy! it's not until closer to 6 months that baby will start to play with an object.
How old is your baby. A baby is usually easy to engage with toys and brightly colored objects. Speak to your pediatrician about vision and hearing problems. Does your baby visually track? Baby at term should. When infants do not pay attention to toys and possessions or faces this is a significant concern that should be discussed with your doctor.