  Electric dipole moments (EDMs) of elementary particles are powerful probes of
new physics with flavor-diagonal CP violation. The reported discrepancy in the
muon anomalous magnetic moment motivates us to explore to what extent new
physics with flavor-diagonal CP violation to address the discrepancy is probed
by searches for the muon EDM. As a benchmark, we focus on a CP-violating
two-Higgs-doublet model to explain the muon $g-2$ anomaly where the muon
exclusively couples to one Higgs doublet. Since contributions to flavor
violating processes as well as the electron EDM are suppressed, the muon EDM
becomes an essential probe of the model. Our result shows that some viable
parameter space leads to the muon EDM of around $d_{\mu} \simeq 6 \times
10^{-23} \, e \, \rm cm$ probed by the PSI experiment and most of the parameter
space is covered by the proposed J-PARC experiment.
