A head should never be machine washed, as it’s the most complex and therefore the most fragile part of your fursuit. The eyes and jaw are particularly exposed.
If your eyes aren’t waterproof, you’ll need to protect them with a cloth or other material that prevents water from reaching them. Be careful not to stick anything on them, as this could damage them.
I recommend soaking the head in cold water with a little soap, holding it by the eye sockets. This way, the eyes will be the highest part, and you can choose not to immerse them. Gently rub and squeeze the fur to remove the water and dirt. Repeat several times. Submerge the parts to be cleaned.
Drain the water, then fill the sink with clean cold water. Squeeze the fur to squeeze out the soapy water. Repeat several times.
Drain the water, then squeeze the fur to remove as much water as possible.
Dry neck-side up on a tumble dryer, so that moisture can escape through the hole.