Arduino AnalogIn minimum current?
From the ATMega328 manual:


  The ADC is optimized for analog signals with an output impedance of
  approximately 10 kOhm or less. If such a source is used, the sampling
  time will be negligible. If a source with higher impedance is used,
  the sampling time will depend on how long time the source needs to
  charge the S/H capacitor, with can vary widely. The user is
  recommended to only use low impedance sources with slowly varying
  signals, since this minimizes the required charge transfer to the S/H
  capacitor.


The same figure goes for any other AVR µC I've dealt with.

If your source has higher impedance you can lower the sampling frequency and/or add a capacitor from ADC-IN to ground to buffer some charge between samplings.