  We study the time-dependent Aharonov-Bohm effect on the noncommutative space.
Because there is no net Aharonov-Bohm phase shift in the time-dependent case on
the commutative space, therefore, a tiny deviation from zero indicates new
physics. Based on the Seiberg-Witten map we obtain the gauge invariant and
Lorentz covariant Aharonov-Bohm phase shift in general case on noncommutative
space. We find there are two kinds of contribution: momentum-dependent and
momentum-independent corrections. For the momentum-dependent correction, there
is a cancellation between the magnetic and electric phase shifts, just like the
case on the commutative space. However, there is a non-trivial contribution in
the momentum-independent correction. This is true for both the time-independent
and time-dependent Aharonov-Bohm effects on the noncommutative space. However,
for the time-dependent Aharonov-Bohm effect, there is no overwhelming
background which exists in the time-independent Aharonov-Bohm effect on both
commutative and noncommutative space. Therefore, the time-dependent
Aharonov-Bohm can be sensitive to the spatial noncommutativity. \draftnote{The
net correction is proportional to the product of the magnetic fluxes through
the fundamental area represented by the noncommutative parameter $\theta$, and
through the surface enclosed by the trajectory of charged particle.} More
interestingly, there is an anti-collinear relation between the logarithms of
the magnetic field $B$ and the averaged flux $\Phi/N$ (N is the number of
fringes shifted). This nontrivial relation can also provide a way to test the
spatial noncommutativity. For $B\Phi/N\sim 1$, our estimation on the
experimental sensitivity shows that it can reach the $\rm 10GeV$ scale. This
sensitivity can be enhanced by using stronger magnetic field strength, larger
magnetic flux, as well as higher experimental precision on the phase shift.
