This paper reports on a search for the electroweak diboson ($WW/WZ/ZZ$) production in association with a high-mass dijet system, using data from proton-proton collisions at a center-of-mass energy of $s=13$ TeV. The data, corresponding to an integrated luminosity of 35.5 fb$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$, were recorded with the ATLAS detector in 2015 and 2016 at the Large Hadron Collider. The search is performed in final states in which one boson decays leptonically, and the other boson decays hadronically. The hadronically decaying $W/Z$ boson is reconstructed as either two small-radius jets or one large-radius jet using jet substructure techniques. The electroweak production of $WW/WZ/ZZ$ in association with two jets is measured with an observed (expected) significance of 2.7 (2.5) standard deviations, and the fiducial cross section is measured to be $45.1\pm 8.6(\mathrm{stat}.)-14.6+15.9(\mathrm{syst}.)$ fb.