No, binary option accounts are not FDIC insured. The accounts are held at brokerages, and many of them are not based in the United States. Never put more money than you can afford to lose in a binary option account, and never keep more money than you need for trading in the account.
Take money out regularly, and stick with reputable brokers. Remember, part of the advantage of trading with binary options is that you do not need to use large positions to make money. Keep your balance manageable, use small positions, and take money out from the brokerage as you earn to limit your risk.