In this paper, a vibration-based method, called wavelet entropy time series, for non-destructive testing of carbon fiber specimens is introduced and demonstrated experimentally. The wavelet transform of vibration signals, acquired after an impact excitation of the specimen, is combined with Shannon’s informational entropy to quantify a trend in the disorder of the signal. Notions such as wavelet entropy, wavelet entropy time series are defined and utilized to assist in structural health monitoring. The scientific merit of the method was investigated both experimentally and computationally. Wavelet entropy time series was able to identify patterns in the complexity of signals making the method suitable for other signal processing applications, outside the scope of non-destructive testing.