For example, before becoming a performance tester I held a Microsoft Certified Systems Engineer (MCSE) certification, had been both a network and systems administrator, had been a data modeler and database designer, had been a configuration manager, and had done some programming and project management. At that time, I didn't even know software testers existed, let alone performance testers.
What I don't recommend is for a functional tester to go to three to five days of vendor training on a performance tool and think they are ready to be a performance tester. The tool is the tip of the iceberg, so to speak. Sure being a master with a tool (or tools, more is better) is extremely valuable, but not until you've really got a good grasp of what to do with it. Tool vendor training simply doesn't do it. In fact, three to five consecutive days of training from anyone doesn't do it.
Performance testing is really all about a way of thinking. Read Jerry Weinberg's Introduction to General Systems Thinking. If you read that and think "Cool, that's how I look at the world!" you're probably well on your way to becoming a performance tester.