How fit do you have to be to start Karate?
To get straight to the point, you don't have to be fit at all.
Nearly everyone who takes up karate isn't "fit" - not by our standards, anyway!
A good instructor will be aware of this and ease you into the training regime. You will not be forced to do things that are beyond your physical capabilities, but you will find that eventually you will be able to do things you never thought you were physically capable of.
If you have an injury, physical disability or illness then the club instructor should know about this. If you are in any doubt about your ability to practise karate visit your Doctor and ask for a report on your current state, and whether (in his/her opinion) you are fit to learn karate.