  Using kinematic maps from the Sloan Digital Sky Survey (SDSS) Mapping Nearby
Galaxies at Apache Point Observatory (MaNGA) survey, we reveal that the
majority of low-mass quenched galaxies exhibit coherent rotation in their
stellar kinematics. Our sample includes all 39 quenched low-mass galaxies
observed in the first year of MaNGA. The galaxies are selected with $M_{r} >
-19.1$, stellar masses $10^{9}$ M$_{\odot} < M_{\star} < 5\times10^{9}$
M$_{\odot}$, EW$_{H\alpha} <2$ \AA, and all have red colours $(u-r)>1.9$. They
lie on the size-magnitude and $\sigma$-luminosity relations for previously
studied dwarf galaxies. Just six ($15\pm5.7$ per cent) are found to have
rotation speeds $v_{e,rot} < 15$ km s$^{-1}$ at $\sim1$ $R_{e}$, and may be
dominated by pressure support at all radii. Two galaxies in our sample have
kinematically distinct cores in their stellar component, likely the result of
accretion. Six contain ionised gas despite not hosting ongoing star formation,
and this gas is typically kinematically misaligned from their stellar
component. This is the first large-scale Integral Field Unit (IFU) study of low
mass galaxies selected without bias against low-density environments.
Nevertheless, we find the majority of these galaxies are within $\sim1.5$ Mpc
of a bright neighbour ($M_{K} < -23$; or M$_{\star} > 5\times10^{10}$
M$_{\odot}$), supporting the hypothesis that galaxy-galaxy or galaxy-group
interactions quench star formation in low-mass galaxies. The local bright
galaxy density for our sample is $\rho_{proj} = 8.2\pm2.0$ Mpc$^{-2}$, compared
to $\rho_{proj} = 2.1\pm0.4$ Mpc$^{-2}$ for a star forming comparison sample,
confirming that the quenched low mass galaxies are preferentially found in
higher density environments.
