The minimum amount of body fat needed for good health is

5% of your body would be fat if needed for good health

Explanation:

In order to maintain good health for your body your body has to be "at least 5% fat" if you're a female your body needs to be made up of "at least 7% of fat." There's something called essential fat which tells you how much fat a person has and with a huge amount of fat your body wouldn't be able to carry out some of the functions or body needs without taking huge amounts of energy which is why being overweight comes with a variety of health issues.

Hope this helps.