Stand very close to a very loud speaker for a few minutes...
Are you going for accurate to life? Create a tone and modulate it to about 16k. But you don't want to make the viewers' ears bleed, so apply in light doses. A basic 1k tone may be too harsh to work with, so you might find a softer sound from a MIDI synth or from a sequencer or keyboard. Maybe like a vibraphone?
A better solution, and this is not knowing the context of the scenario, might be to go interpretive. Layer a few higher-pitched tones together, and be creative with the tones. Start with one, and then bring the others in after (to portray the total effect setting in). To accentuate it even more, if it fits the scene, take all the dialog outside the actor's head and roll all the highs and high-mids off, giving his/her surroundings a muffled sound.
Some wireless microphone packs have a pilot tone that basically simulates that as well... i'm not sure of a good way to can that audio, but it's possible...
Basically 75% of individuals have a tinnitus match frequency above 3500hz so you might want to try that as a starting point and play until you get the right sound. Personally I would use a tone generator built into your NLE (probably sine wave )if it has one, because in my experience (fireworks, etc) the sound IS annoying and a pure tone, not something more complex.
Depending on how the tinnitus is being played in the scene (is it constant? is it immediate onset from the result of an explosion, etc) you might find some movies to use as inspiration. It seems to me like there are several instances of the explosion induced tinnitus thing going on in Saving Private Ryan for example.