We don't know if massless particles may have a wavelength beyond planck length, but there are some significative indices (including the ones provided in the other answers) against limitation of wavelength. In particular, according to Wikipedia,

There is currently no proven physical significance of the Planck length; it is, however, a topic of theoretical research.

This research is referring in particular to the discreteness of spacetime and not to wavelengths.

The possibility to increase the relative velocity of an observer is an essential argument, and it is important to note that the spacetime interval of massless particles is zero. A zero interval means that there is no place for a n y kind of wavelength, even not for a wavelength smaller than Planck length. However, contrary to space intervals, the spacetime interval does not correspond to any observer but to a (hypothetical, non existent) observer moving at speed of light. You can now assume an observer moving very close to speed of light, and as far as we know today there is no limit, that means the observer will never reach speed of light, but he may come arbitrarily close to it, and this observer would observe a wavelength which may be arbitrarily small, that means arbitrarily close to the zero length of the zero spacetime interval of the massless particle.

Now, the speed of the observer is a space interval per time interval, and by this, your question transforms into the question if wavelengths are discrete, in particular if space and/ or time are discrete. But as I mentioned above, mainstream today considers space and time to be continuous.

We don't know if massless particles may have a wavelength beyond planck length, but there are some significative indices (including the ones provided in the other answers) against limitation of wavelength. In particular, according to Wikipedia,

There is currently no proven physical significance of the Planck length; it is, however, a topic of theoretical research.

This research is referring in particular to the discreteness of spacetime and not to wavelengths.

The possibility to increase the relative velocity of an observer is an essential argument, and it is important to note that the spacetime interval of massless particles is zero. A zero interval means that there is no place for a n y kind of wavelength, even not for a wavelength smaller than Planck length. However, contrary to space intervals, the spacetime interval does not correspond to any observer but to a (hypothetical, non existent) observer moving at speed of light. You can now assume an observer moving very close to speed of light, and as far as we know today there is no limit, that means the observer will never reach speed of light, but he may come arbitrarily close to it, and this observer would observe a wavelength which may be arbitrarily small, that means arbitrarily close to the zero length of the zero spacetime interval of the massless particle.

Now, the speed of the observer is a space interval per time interval, and by this, your question transforms into the question if admitted wavelengths are discrete, in particular if space and/ or time are discrete. But as I mentioned above, mainstream today considers space and time to be continuous.