Tinnitus can be caused by so called ototoxic drugs. Generally, it is chemical intoxication of neurosensory cells in the inner ear (see eg. this article on ototoxicity).
Among ototoxic drugs are certain types of stronger antibiotics or chemotherapeutic drugs containing heavy metals (eg. cisplatin containing platinum).
The principle of damage is more or less similar to the acoustic trauma. Toxic effect of drug damages the metabolism of the cell and its functions, causes degeneration of the stereocilia and finally apoptosis of the whole cells. Those that survived the programmed death due to an injured metabolism, transmit false signals to the auditory center of the brain - thus causing tinnitus.