The wrap can support baby's head but doesn't have to cover it.
Before your baby reaches 4 months:
The wrap must support his head (in a Vertical / Seated Cradle Carry with a one month-old for example) from behind his neck, especially if you're walking and he's asleep.
In front carries, with his spine in a curve, his head is naturally supported as it lies against the wrapper (be careful to relieve tensions as it falls to his chest or turns to the side).
Baby's airway should be clear at all times.
After 4 months, when baby has good head control:
As his neck becomes more mobile, he probably won't like having fabric on his head when he's awake, but you can try and put the wrap on his head when he is asleep.
