Please excuse the phrasing, which is not scientifically rigorous. The post only serves as a starting point.
Any electric current (the net movement of electrons) induces an magnetic field, and any magnetic field in turn induces an electric field. Indeed, each other is just one side of the same coin. The first to join these two into what is known as electromagnetism was JC Maxwell in his four fundamental equations.
Biomagnetism results from the flow of electricity within special functional tissues, located in organisms. (Some organisms have pure electrical junctions rather than 'interconnects' which rely on chemical messengers as vertebrae do. See this classical paper, and Evolution of nervous systems )
Certain heavy atoms have asymptotic magnetic field effects (a thankful property for many NMR structural biologists).
As such, even if a metalloprotein with such heavy metal-atoms were to move inside the virus, driven for instance by a chemical oscillator (which would eventually come to a standstill), the effect would really have to be theoretically predicted first, and then empirically measured, rather than coincidentally just discovered (like say Penicillin). That is because it is very expensive to do science at such small scales, and the required hardware and human resources are in competition with projects that promise greater outlooks.
My answer would be another question:
What sense would it make for a terrestrial virus to potentially benefit from producing an electric current inside, to motivate theoretical scientists to look into such a matter?
Or, what virus features would account for the sufficient flow of electricity to be considered a mechanism ( - as the magnetism at these scales is just the 'side effect') ?
( During the life-cycle of a typical virus, the virus does produce a magnetic effect, as the information-carrier molecule is charged, and the production of a new virus requires the net transport of charged molecules. Note, that by convention viruses are not living entities. )
Afaik, the field of biomagnetism only really took off due to the invention and commercialization of the SQUID.
This is just a starting point, motivated by the challenged notion of viruses. Virologists have a much better and up-to date grasp on the matter.
Killing a virus:
On a less serious side-note, one way to kill any virus is to put it on a Magnetar.
I hope this helps as a starting point...