We report the frequency stabilization of an erbium-doped fiber distributed-feedback laser using an all-fiber-based Michelson interferometer of large arm imbalance. The interferometer uses a 1 km SMF-28 optical fiber spool and an acousto-optic modulator allowing heterodyne detection. The frequency-noise power spectral density is reduced by more than 40 dB for Fourier frequencies ranging from 1 Hz to 10 kHz, corresponding to a level well below 1 Hz2/Hz over the entire range; it reaches 10(-2) Hz2/Hz at 1 kHz. Between 40 Hz and 30 kHz, the frequency noise is shown to be comparable to the one obtained by Pound-Drever-Hall locking to a high-finesse Fabry-Perot cavity. Locking to a fiber delay line could consequently represent a reliable, simple, and compact alternative to cavity stabilization for short-term linewidth reduction.