The detection of spatially extended line emission in multiply imaged QSOs offers a new possibility to study the properties (kinematics and structure) of the ionized gas in the host galaxies of high-redshift QSOs. We have studied the arc of extended emission detected in Q2237+0305, finding that it arises from the core of the C III] λ1909 emission line and that the emission in the wings is compact. From the morphology of the emission-line profiles we have identified an additional narrow emission line component affecting the core of the spectra in the region of the arc (around component D). The kinematic analysis shows that the extended narrow-line region (NLR) exhibits broadening similar to that of NLRs in Seyfert galaxies and that its mean velocity is consistent with galaxy rotation. We model the shape of the arc and thus derive qualitative lower and upper limits for the source of ionized gas in the host galaxy of the QSO. Thus, thanks to the lensing, we resolve kinematically and spatially an extended NLR of the quasar host that is likely photoionized by the central engine.