Self-similarity or scale-invariance is a fascinating characteristic found in various signals including electroencephalogram (EEG) signals. A common measure used for characterizing self-similarity or scale-invariance is the spectral exponent. In this study, a computational method for estimating the spectral exponent based on wavelet transform was examined. A series of Daubechies wavelet bases with various numbers of vanishing moments were applied to analyze the self-similar characteristics of intracranial EEG data corresponding to different pathological states of the brain, i.e., ictal and interictal states, in patients with epilepsy. The computational results show that the spectral exponents of intracranial EEG signals obtained during epileptic seizure activity tend to be higher than those obtained during non-seizure periods. This suggests that the intracranial EEG signals obtained during epileptic seizure activity tend to be more self-similar than those obtained during non-seizure periods. The computational results obtained using the wavelet-based approach were validated by comparison with results obtained using the power spectrum method.