There are at least FIVE sources of "noise" in an analog multiplexer.
1) noise from the VDD supplies, that noise appearing on gates of the MOSFET switches; assume each gate is 100pF capacitance from the VDD into your signal path
2) noise from the digital control signals (MicroController outputs are never quiet, unless you shut off the MCU clocking); these 1 nanosecond transients (0.5 volt amplitude) inject charge and that charge explores all possible paths back to the MCU. This exploration makes the inductors ring, in GND pin, in VDD pin, and elsewhere. Even in clean-VDD situations, this need-a-return-path charge movement causes the VDD and the GND to constantly be ringing
3) charge injection from switching; to reduce this impact, have very low source and load impedances; this means have capacitors on both input and output pins
4) the "noise" from not yet accurately settled channel switching; every TAU of setting provides another NEPER, or 8.6 dB of improved accuracy (about 1.6 bits better ENOB)
5) the genuine FET channel thermal/Johnson/Boltzmann random noise; 1 K ohm Ron provides 4 nanovolts per rootHertz; a 1 Kohm channel and 159pF Cload is a 159 nanosecond Tau and is exactly 1MHz bandwidth. A 1 MHz bandwidth at 4 nanoVolts/rtHz becomes 4,000 nanoVolts (4nV * sqrt(1,000,000)) or 4 microVolts RMS noise floor. [there is a PI/2 error here; you may ignore that for now; this factor comes from the gradual attenuation of any 1-pole RC filter]