You absolutely can — and in two different ways, depending on your preference.
The first is to place the noodles and cold water into a microwaveable bowl, and microwave on high for about 2-3 minutes, total. It can help to stir or "flip" the noodles halfway through. If the noodles aren't done to your satisfaction, continue microwaving them in 30-60 second intervals. Once heated through, add your flavor packet, stir and eat.
The other is to simply use the microwave to boil your water. Put your water in a microwave-safe vessel and microwave for a few minutes. It is a good idea to let it sit for a minute before moving it out of the microwave (microwave-boiled water can superheat without looking like it's boiling... be safe). Pour your boiled water over the noodles and flavor packet and cover. I often cover the bowl with a plate of the appropriate size. Let it sit for 3-5 minutes. Stir and eat.