What is the best way to rectify 1MHz, 50V 0.1% duty cycle signal?
Where have you found a metal plate oscillating at 1MHz? That's well into the ultrasound range. Something is putting quite a lot of energy into driving that plate.

First, lets think about how much power you actually have. A piezo transducer is basically a capacitor, which charges up when it's bent/squashed.  The energy stored in the capacitor is:

$$E=\frac{1}{2} C V^2 $$

So even if your transducer is only somewhere around 1nF, each oscillation of the plate is getting you 1.2μJ.  At 1MHz that's 1.2W (!) but at 0.1% duty your power is 1.2mW. Far more than a microcontroller needs, so you can afford to be pretty inefficient.

The first step is to rectify that ac signal. You'll need some diodes with a low reverse recovery time, suitable for 1MHz. Then you need a capacitor for storage, it needs to be big enough to last over the 999ms when the plate isn't moving, but also have a self resonance well over 1MHz to charge effectively. In reality, you'll better off with a small ceramic and a beefy electrolytic in parallel. Then you need to regulate down to 5V - a zener works, but wastes most of the power. A linear regulator is the same. A little switching regulator would be more efficient, and a power management IC would work well and offer a few extra features.

Rather than building it yourself, you might be able to find an IC that does all the hard work. Several companies make ICs specifically for harvesting energy from piezos. 1MHz is a very high frequency though, so you might not find anything suitable.

Either way, you'll have to be careful about how you lay out your circuit. That transducer is going to be kicking out tens of milliamps at 1MHz. If there is any length of cable between the transducer and the rectifier, it's going to radiate like crazy. But at the same time, you don't want to stick your circuit directly onto a vibrating plate or it'll have a short life. You might want to move the microcontroller a short distance away from the rectifier and/or shield it.