Is Kawasaki disease infectious?

No. But keep others who may have a cold or any signs of illness away from the child (I'm assuming it is a child. Most, if not all inflicted with Kawasaki's are young children/infants) with Kawasaki's. Much like you would keep others who may be sick away from a newborn. Otherwise healthy individuals are safe to the person with Kawasaki's and the child with Kawasaki's is not a threat to healthy individuals.

The child with Kawasaki's immune system is weak, so it is important that any healthy individual who is coming near the child washes their hands beforehand.

I wish you the best!

I don't think it is, and Wiki doesn't think so either.

Not treated with antibiotics, anti-virals or anti-candidal medications, a good reason not to count it in infectious diseases. Altough it is a great immetator for infection.

No.

Kawasaki disease is the most common form of vasculitis that primarily affects children. The disease produces irritation and inflammation of many tissues of the body, including the hands, feet, whites of the eyes, mouth, lips, and throat. High fever and swelling of the lymph nodes in the neck also are characteristic of this illness. The inflammation is uncomfortable, but resolves with time. However, the main threat from Kawasaki disease comes from its effect on the heart and blood vessels. Heart-related complications can be temporary or may affect the child long-term. The heart, particularly the coronary arteries, is affected in as many as 20 percent of children with Kawasaki disease. Kawasaki disease is fairly common in the US. According to the American Heart Association, the illness is a major cause of heart disease in children. About 1,800 new cases are diagnosed in the US each year, and the incidence is on the rise. Kawasaki disease, together with acute rheumatic fever, is the leading cause of acquired heart disease in children in the US and Japan. It is not clear what causes Kawasaki disease. Scientists believe a virus may be responsible, but current research is still underway. Kawasaki disease does not appear to be contagious, nor does it appear to be hereditary. Specific treatment for Kawasaki disease will be determined by your child's physician based on: your child's age, overall health, and medical history, extent of the disease, your child's tolerance for specific medications, procedures, or therapies, expectations for the course of the disease, your opinion or preference. Currently, there is no known way to prevent Kawasaki disease.
Hope this helps,
Matador 89