We present analytical theory of dissipative soliton absorption spectroscopy. A dissipative soliton formed in an all-normal-dispersion oscillator with a narrowband intracavity absorber acquires spectral features that follow the index of refraction of the absorber, as confirmed by numerical simulations and experimental evidence. In contrast to the soliton absorption spectroscopy in an anomalous dispersion regime, we anticipate resonant enhancement of a modulation signal near the pulse spectrum edges that results in an additional signal gain. We further show that the pulse acquires a nanosecond-long tail in the time domain and provide simple formula for estimation of its energy content.