Can low-frequency electromagnetic radiation be ionizing?
Background:
Einstein's photoelectric effect theory won him the Nobel prize, and it relates very closely to this. Although it's different from photoionisation, it relies on similar ideas.
His proposition: each atom will absorb the energy of one photon, and the energy of a photon is given by $$E=h\nu$$where $h$ is Plank's constant, a really, really tiny number ($6.62607004 × 10^{-34} m^2 kg / s$), and $\nu$ is frequency of the light. Higher intensity light, which is analogous to wave amplitude, contains more photons, but the energy of each photon is the same for a given frequency.
If I shine low-frequency high-intensity light on a surface, there's plenty of energy, but each atom, upon absorbing one photon, won't be able to lose an electron. However, if I shine high-frequency light, even if the intensity is low, each atom which absorbs a photon will be able to loose an electron, and we see ionization.
But when the intensity is high enough, even low frequencies will cause ionization.
This phenomenon, called multi-photon ionization, occurs when the atom absorbs more than one photon. It's usually pretty rare, because an atom frequently emits the other photons before it absorbs enough energy totally, but at very high enough intensities, it's appreciable.
Sound works differently in air: we generally don't say it's quantized in the same way, although if you examine it more minutely, you'll see that it can be quantized as phonons, which aren't evident in gases. But that's not relevant to your question, it's just something to keep in mind if you want to generalize a bit more by discussing sound in condensed matter.
Oddly enough, the parallel to sound and hearing loss is wrong! See this Biology SE question... high-frequency sounds are dangerous not particularly because they have more energy (which they do, see the equation for sound energy in a container), but because of the nature of the human ear and the alignment of hairs in it.
All frequencies of light can be ionizing. Even a static (zero frequency) field can rip the electrons off atoms if strong enough.
However, when we talk about ionizing radiation, we're usually thinking about quantum effects. In quantum mechanics both sound and light are quantized, into phonons and photons respectively, with energy $$E = \hbar \omega$$ each. And a classical light wave or sound wave is simply a coherent state of many photons/phonons stacked on top of each other.
Light sources with frequency $\omega$ high enough for the energy of a single photon to ionize a single atom are thus especially dangerous, because you can still get hurt even if the total energy of the photons is very low. That is, you can get hurt by X-rays without noticing anything, but you can't get hurt by microwaves without noticing; a single microwave photon has too little energy to do anything. The only way to get hurt by a microwave is for it to heat you up, by interaction with a strong classical microwave field, and there's no way to not notice that.
Sound isn't dangerous in the way that X-rays are. First off, we typically live in air, and a gas like air behaves too messily to really have phonons (see discussion here) at all. Even if air did support phonons, the frequencies the phonons can have are bounded by how fast the air molecules can oscillate to form a sound wave -- more precisely, the wavelength must be much greater than the mean free path. This places an extremely low frequency limit relative to light, so one phonon is always harmless.
While it is true that high-frequency sound is more dangerous, all discussion about the effects of sound on humans is firmly in the classical regime. That is, the danger of high-frequency sound has absolutely nothing to do with the fact that high-frequency phonons have more energy.
A multi kW powered CO2 laser can easily strip an atom of many electrons. Such lasers are used to generate extreme ultraviolet (EUV) light for computer chip manufacturing. In such light sources tin atoms are stripped of 10-12 electrons. The subsequent recombination produces EUV light.