When my kids were little, I would wash their stuffed animals one of these two ways:
Valuable, vintage or delicate stuffed animals:
Surface wash with a clean damp cloth and mild soap. Air dry and gently brush or “fluff” it when dry to renew its fur.
New or stuffed animals in overall great condition:
Stuffed animals in sound physical condition can be washed in the washing machine. Place the stuffed animal into a clean pillow case and tie a knot in the case to prevent the toy from falling out. Wash on the gentle cycle using cold water. Air dry and gently brush or “fluff” it when dry to renew its fur.