A child's ability to play instruments is closely related to their physical development. While rhythmic skills develop as early as the first year of life, the muscle coordination required for playing an instrument doesn't come till much later. Something as simple as playing a short melody on the piano requires enough motor skills and coordination to use the eyes, ears, and muscles in the fingers, hands, and forearms, all in tandem.
This is the developmental sequence for Playing instruments:
Children of less than two years can rock, nod, and sway to a beat. They have the ability to grasp objects, making them able to play rattles and jingle bells.
From ages two to three, children start having short periods of rhythmic regularity. This gives them the ability to play the hand drum and rhythm sticks.
From three to four, children have longer periods of rhythmic regularity, a sensitivity to pulse, and can sway their arms. They can now play the claves, woodblock, tambourine, guiro, maracas, gong, cowbell, and play the rhythm sticks by rubbing them.
From five to six, children start to be able to maintain a pulse, alternate their hands, and have basic eye-hand coordination. This allows them to play the finger cymbals, bongo drums, timpani, cymbals, triangle, and even the keyboard with one hand.
From seven to nine, children have developed eye-hand coordination. This allows them to play a wide range of things, including different pitched instruments such as the xylophone, the keyboard with both hands, the recorder, and the autoharp.
From age ten to twelve, eye-hand coordination has become much easier, as well as finger flexibility and control of the breathing apparatus. They can now play melodies on the xylophone and keyboard, more notes on the recorder, chords on the guitar, and even orchestral winds and brass.