Continuous glucose monitoring (CGM) can inform diabetic people of the status of their glucose and warn of actual or impending hypo- or hyperglycemia. In the past decades, biosensors have been developed for CGM, among which the subcutaneously implanted glucose monitors are of much interest because they are less painful while quickly measure the critical glucose concentrations in the body. Experiments of these monitors show that there are occasionally spurious dropouts which do not reflect the true glucose level and will cause problems in glucose calibration. In this paper, a discrete wavelet transform (DWT) based online detector is proposed to detect dropouts for a single glucose sensor signal. Its effectiveness is demonstrated by both experimental data from the non-diabetic pig and clinical data from people.