What you're seeing is a subharmonic. It's generally a sign of instability. Basically, through clipping or some other mechanism, the amplifier's "state" is not the same at a given point on each cycle of your waveform.
So you're feeding this kind of signal in and expecting a similar output:
-- -- -- -- -- -- -- -- --
\ / \ / \ / \ / \ / \ / \ / \ /
-- -- -- -- -- -- -- --
But what is coming out looks more like:
-- --- -- --- -- --- -- --
\ / \ / \ / \ / \ / \ / \ /
-- --- -- --- -- --- --
(I'm guessing here; can't see your scope, if any.) Note that this signal repeats every two cycles. So it's more like a 9 kHz signal with an 18 kHz second harmonic.
One possible solution would be to first feed the signal through another amplifier to gain up the signal by at least 10, then have its output go to the LM386 which would only need to be at a gain of 2. If you want a volume control, vary the gain of the first amplifier.
EDIT: Just remembered that even-numbered harmonics are usually signs of asymmetry across the x axis, i.e. the top half of the waveform doesn't look like the bottom half. Not sure how to draw it, though.