Great question (as measured by the number of discussions it raised)! 

After looking into this question and discussing for quite a while with @Justin - I am, however, afraid I cannot give a conclusive answer.

Firstly, I was not able to find any literature that investigated duration thresholds on tone bursts or auditory clicks, let alone as a function of acoustic frequency.  

That having said, we can start off by looking at **auditory clicks**, which are generally the shortest possible well-defined auditory stimuli. The shortest auditory click I was able to find, and which was used in a psychophysical context (i.e., audible to a human) was **10 microseconds** ([Leshowitz, 1971][2]). 

Now, (1) assuming 10 microseconds is the lower duration limit of a click (it may well be lower), and (2) assuming this click duration is representative of the lower limit of a tonal burst duration limit (it may well not be), and (3) assuming you indeed wish to know about/use auditory tones and not clicks, and finally (4) assuming we need at least one wavelength of a tone to fit in this window, then we could present a frequency of 100 kHz, or higher. As 20 kHz is the upper frequency limit of the human ear, we would need at **least 50 microseconds** for one wavelength, i.e., basically what @Justin concluded, but it does not end here:

*Frequency splatter* ([Fishbach et al., 2001][1]) limits the lower limit of tonal stimuli. To prevent spectral splatter one needs to incorporate rise and fall times (ramps) onto the tonal stimulus. Hence, again assuming you do want tonal stimuli, an onset and offset ramp of one wavelength each would be advisable (at the very least) and hence 3 wavelengths are needed, increasing the duration of a 20 kHz tone to 3 wavelengths, i.e., **150 microseconds** (spectral splatter may not be prevented, but at least reduced).  

On top of this theoretical approach, it has to be noted that I started off with taking a click as a starting point. A click, being an impulse signal, basically stimulates the entire cochlea (the inner ear), and hence represents the most powerful auditory stimulus. Pure-tone bursts are, as a consequence, weak stimuli as they stimulate a small proportion of the available hair cells. High sound levels may therefore be necessary for short tonal stimuli, in turn degrading the frequency resolution in the cochlea as excitation spreads away from the characteristic frequencies. Mostly, several milliseconds are used as tone bursts. 

Moreover, taking 20 khz is kind of an upper limit, and many folks are not even able to hear 16 khz. An upper limit of, say, 12 kHz would be advisable when grownups are used. This means a wavelength of 83 microseconds and for 3 wavelengths (for ramp times) that means **250 microseconds**.

If lower frequencies are needed, this number would increase further.

I hope this theoretical approach helps you somewhat, but it is highly advisable to start testing minimal durations and think about whether clicks would suffice your purpose, which would make life a lot easier (but less informative as well).

<sub>**References**</sub>  
<sub>[Fishbach et al. J Neurophysiol 2001; 85:2303-23][1]</sub>  
<sub>[Leshowitz et al. J Acoust Soc Am 1971; 49, Suppl 2:462-6][2]</sub> 

  [1]: http://www.math.tau.ac.il/~hezy/papers/j28.pdf
  [2]: http://scitation.aip.org/content/asa/journal/jasa/49/2B/10.1121/1.1912374