A measurement of the Higgs boson production cross sections via associated $WH$ and $ZH$ production using $H \rightarrow WW^{\ast} \rightarrow \ell\nu\ell\nu$ decays, where $\ell$ stands for either an electron or a muon, is presented. Results for combined $WH$ and $ZH$ production are also presented. The analysis uses events produced in proton-proton collisions collected with the ATLAS detector at the Large Hadron Collider in 2015 and 2016. The data correspond to an integrated luminosity of 36.1 fb$ ^{-1}$ recorded at a centre-of-mass energy of 13 TeV. The products of the $H \rightarrow WW^{\ast}$ branching fraction times the $WH$ and $ZH$ cross sections are measured to be $0.67^{+0.31}_{-0.27}$(stat.)$^{+0.18}_{-0.14}$(syst.) pb and $0.54^{+0.31}_{-0.24}$(stat.)$^{+0.15}_{-0.07}$(syst.) pb respectively, in agreement with the Standard Model predictions.