  We build string backgrounds for Yang-Baxter deformations of the
$AdS_4\times\mathbb{CP}^3$ superstring generated by $r$-matrices satisfying the
classical Yang-Baxter equation. We obtain the metric and the NS-NS two-form of
the gravity dual corresponding to noncommutative and dipole deformations of
ABJM theory, as well as a deformed background with Schr\"odinger symmetry. The
first two backgrounds may also be found by TsT transformations while for the
last background we get a new family of non-relativistic ABJM theories with
Schr\"odinger symmetry.
