What minimum knowledge should one possess to start his/her career in data science/analytics?

I’m going to diverge slightly from the other answers. If your goal is to enter analytics as a discipline and don’t necessarily need to start with the DS title I would suggest the following: sql and python. Learn them and learn them really well. Moreover learn to solve actual problems with them and be prepared to talk about them.

The standard DS/ML curriculum focuses heavily on the skills the others have enumerated on their excellent posts. However I often find candidates who have drilled those curricula but can’t do the basics and solve problems and tell me why the problems matter for the business.