Processor's speed of a computer is measured in

CPU speed is the central factor in a computer's performance. And this CPU speed depends on the processor in the CPU chip. In a computer, clock speed refers to the number of pulses per second generated by an oscillator that sets the tempo for the processor. Clock speed is usually measured in Hertz (Hz).

But now-a-days, a pure processor's performance is measured in MIPS (Millions of Instructions Per Second). As here in the question, how a processor's speed is measured is asked and it is Hertz. 

Hence, Processor's speed of a computer is measured in Hertz(Hz) [MHz, GHz].