Are meteorites radioactive?
Only very slightly, and not dangerously. Like all rocks they contain traces of natural radioactive elements, and cosmic rays in space create a few extra radioactive atoms, but the levels are tiny and safe to handle.
Almost everything around us is a little radioactive, including soil, building stone, bananas and our own bodies. Rocks contain small amounts of naturally radioactive elements such as uranium, thorium and a form of potassium. Meteorites contain these too. In fact, the commonest meteorites, the chondrites, generally contain much less uranium and thorium than granite, a rock used in many buildings.
Meteorites also carry an extra kind of radioactivity picked up in space. While a meteoroid travels between the planets, it is bombarded by cosmic rays, high-energy particles from the Sun and from beyond the Solar System. These smash into atoms in the rock and create new ones called cosmogenic nuclides. Some are radioactive, for example aluminium-26 and beryllium-10, which decay over hundreds of thousands to millions of years. The amounts are minute. Earth's atmosphere shields rocks on the ground from most cosmic rays, so this effect is unique to material that has spent time in space.
That faint signal is a gift to scientists. By measuring cosmogenic nuclides, they can work out how long a meteoroid travelled through space as a small body, its cosmic-ray exposure age, and how long it has been on Earth since it fell. In fresh falls, very short-lived nuclides, which decay within days to a few years, can reveal how big the meteoroid was before it entered the atmosphere. Measuring them requires extremely sensitive detectors, sometimes in shielded underground laboratories, precisely because the signal is so weak.
So there is no need to worry about radiation from a meteorite on your shelf. Ordinary care is enough: keep specimens clean and dry, wash your hands after handling, and don't lick or cut them.