This is entirely expected behaviour (!)
You have a radio transmitter (GSM module) right next to a sensitive analog circuit - this means you are injecting RFI (radio frequency interference) into the analog circuit. You have to keep the radio emissions away from your analog circuit - this means shielding and/or distance. You also need to pay close attention to layout within your analog circuit to make it less susceptible to RFI - this is rather a complex concept to get across in a short post though.
Briefly you should try and arrange your analog circuit on a ground plane, and ensure there are no loops (ie run a signal wire right next to its ground return - preferably in a twisted pair or as a shielded coax cable).
If the GSM shield can use a remote aerial this can help. You ideally want the entire circuit in a metal box with only the aerial sticking out.