Can thyroid disease be passed on to my child, as if it were contagious?

Pass on. Certain thyroid disease can increase your children risk of getting the disease but it is not contagious.
Thyroid. The good news: your thyroid problem is not contagious. The bad news: there is likely a genetic component. All first-degree relatives of a thyroid patient should be screened for predisposition. This just means a lab test to measure both antibodies and function.