The elliptic flow of muons from the decay of charm and bottom hadrons is measured in $pp$ collisions at $\sqrt{s}=13\text{ }\text{ }\mathrm{TeV}$ using a data sample with an integrated luminosity of $150\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$ recorded by the ATLAS detector at the LHC. The muons from heavy-flavor decay are separated from light-hadron decay muons using momentum imbalance between the tracking and muon spectrometers. The heavy-flavor decay muons are further separated into those from charm decay and those from bottom decay using the distance-of-closest-approach to the collision vertex. The measurement is performed for muons in the transverse momentum range 4--7 GeV and pseudorapidity range $|\ensuremath{\eta}|<2.4$. A significant nonzero elliptic anisotropy coefficient ${v}_{2}$ is observed for muons from charm decays, while the ${v}_{2}$ value for muons from bottom decays is consistent with zero within uncertainties.