Gamma radiation from the Crab pulsar wind nebula (PWN) shows significant variability at $sim100$ MeV energies, recently revealed with spaceborne gamma-ray telescopes. Here we report the results of a systematic search for gamma-ray flares using a 7.4-year data set acquired with the Fermi Large Area Telescope. Analyzing the off-pulse phases of the Crab pulsar, we found seven previously unreported low-intensity flares (small flares). The small flares originate from the variable synchrotron component of the Crab PWN and show clearly different features from the steady component of the Crab PWN emission. They are characterized by larger fluxes and harder photon indices, similar to previously reported flares. These flares show day-scale time variability and imply a strong magnetic field of $B_{rm min}approx 1~mathrm{mG}$ at the site of the gamma-ray production. This result seems to be inconsistent with the typical values revealed with modeling of the non-thermal emission from the nebula. The detection of the small flares gives a hint of production of gamma rays above $100$ MeV in a part of the nebula with properties which are different from the main emitters, e.g., due to bulk relativistic motion.
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