Between the age of three and six ought to be fine for your child to accompany you to an art museum. If your child is obedient enough to follow your instructions regarding touching of art pieces and not running wild, then you should have an enjoyable outing. If you have to constantly admonish your child in the museum for unruly behaviour, you may be asked to leave by the security guards.
Try to establish your child's interest in art before you go, via looking at art work in books, or on computer slide shows. When you go to an art exhibition or museum with your child, make the experience interesting, by getting your child to point out recognisable objects, shapes and colours that are depicted in pictures and sculptures.
If your child is a bit older, you can start explaining symbolism used in art and the emotional effect of different colours, lines and textures.
Try to establish your child's interest in art before you go, via looking at art work in books, or on computer slide shows. When you go to an art exhibition or museum with your child, make the experience interesting, by getting your child to point out recognisable objects, shapes and colours that are depicted in pictures and sculptures.
If your child is a bit older, you can start explaining symbolism used in art and the emotional effect of different colours, lines and textures.