Have you just tried it to see if the warning goes away?
Do you leave the system powered constantly or for very long periods, especially unattended? Usually, those warnings are for high-duty cycle systems as most people will become aware that the fan failed while using it. You can set a fan speed that you can hear but isn't intrusive, so if it goes away you'll know it; that's usually best anyway.
Usually a BIOS will spin up all fans at boot to test them (part of POST); Is the CPU fan not spinning up during that time? Do chassis fans? If not, I'd be wondering if your CPU Cooler/Fan has a built-in temp sensor that won't turn the fan on until the CPU warms up. If so, it can't spin up even if the BIOS commands when starting cold.
What CPU cooler are you using? Is this a recent change in behaviour? or has it always done it?