Fermi-LAT's detection of {gamma}-rays from narrow-line Seyfert 1 galaxies (NLS1s) has received increasing attention. Understanding these {gamma}-NLS1s is of interest because they have some properties similar to blazars, which are known to show rapid and large-amplitude variability. Based on the largest sample of {gamma}-NLS1s (25 sources), we carried out a systematic search for rapid mid-infrared (MIR, 3.4 and 4.6{mu}m) variability using the multiepoch data of the Wide-field Infrared Survey Explorer (WISE). We also compared a few variability properties between {gamma}-NLS1s and {gamma}-ray blazars. Our main results are as follows. (1) Thirteen {gamma}-NLS1s showed significant (>3{sigma}) rapid variability in at least one of the two MIR bands. The MIR emission of these sources is dominated by the synchrotron emission of relativistic electrons in the jet. (2) The {gamma}-NLS1s with flat radio spectra are more variable than those not detected in {gamma}-rays. (3) The {gamma}-NLS1s tend to show smaller amplitude of variability as well as lower duty cycle relative to {gamma}-ray blazars. (4) The {gamma}-NLS1s tend to show a trend of bluer-when-brighter on both intraday and long timescales, similar to {gamma}-ray blazars. (5) The {gamma}-NLS1s that are more variable on long timescales have larger amplitudes of variability and higher duty cycles on intraday timescales. (6) In the majority of cases, the {gamma}-NLS1s fall in the WISE Gamma-ray Blazar Strip (WGS). However, we noted migrations outside of the WGS due to significant variability.