This is a fascinating question and not easy to answer because microwave ovens are extremely complex and not as well understood as you might think. Anyway, here are some thoughts.
First, you have to understand that microwaves are a form of electromagnetic energy, just like visible light, TV, radio, X-rays, etc. Each of these is distinguished by its frequency and associated wavelength. For the microwave oven the nominal (average –it’s really a range) frequency is 2450 Megahertz (MHz) or million of cycles/second, or 2.45 Gigahertz (GHz) billions of cycles/second; and this has an associated “free space” wavelength (effectively air or vacuum) of 12.2.cm. The wavelength decreases as it passes through an absorber such as water where the wavelength at room temperature is a bit over one cm. It’s called an electromagnetic wave because it has an electrical component and a magnetic component – both have to be there – one can’t exist without the other. It is the electrical component that heats things like water, food, oils, etc. The magnetic component heats magnetic materials such as iron (ferrous) containing materials.
The answer to your question is very complex because there are so many factors (I originally wrote an answer early this morning but, because I am new to this site, it got lost in never-never land. Since then I’ve thought of more things). The thing that stands out in my mind is the relative volume of water & metal. Let’s say you have a liter of water in a glass beaker and you place a small magnet on the center bottom. It is unlikely the magnet would get any microwave energy because the water would have absorbed all of it since the penetration depth of microwaves into water at room temperature (the distance at which 63% of the energy is absorbed and causes heating) is a little more than a centimeter. I’m neglecting microwave energy coming through the center bottom of the beaker – very complex! So, all the microwaves heat the water….. But now, let’s assume the magnet’s volume is large enough to come within a centimeter of the glass side wall – first microwaves would be absorbed by the water, but there is likely to be sufficient microwave energy left to heat the magnet. It sounds good, but there are lots of complications. For example, if the magnet is that large, then there isn’t much water so the magnet will be heating a small volume of water and that represents a particular case of the problem. I suggest you consider how you would experiment to learn the answer. A warning – I’ve been thinking about how to run the experiment and it is very difficult. I’d be happy to try t help you. Good luck! By the way, it couldn't possibly arc - the electric field energy would be far too small because of the water.