Context. The dark cloud Lynds 723 (L723) is a low-mass star-forming region where one of the few known cases of a quadrupolar CO outflow has been reported. Two recent works have found that the radio continuum source VLA 2, towards the centre of the CO outflow, is actually a multiple system of young stellar objects (YSOs). Several line-emission nebulae that lie projected on the east-west CO outflow were detected in narrow-band Hα and [S ii] images. The spectra of the knots are characteristic of shock-excited gas (Herbig-Haro spectra), with supersonic blueshifted velocities, which suggests an optical outflow also powered by the VLA 2 YSO system of L723. Aims: Our aim is to study L723 in the near-infrared and look for line-emission nebulae associated with the optical and CO outflows. Methods: We imaged a field of ~5' × 5' centred on HH 223, which includes the whole region of the quadrupolar CO outflow with narrow-band filters centred on the [Fe ii] 1.644 μm and H2 2.122 μm lines, together with off-line Hc and Kc filters. The [Fe ii] and H2 line-emission structures were identified after extracting the continuum contribution, if any. Their positions were determined from an accurate astrometry of the images. Results: The H2 line-emission structures appear distributed over a region of 5.5 arcmin (~0.5 pc for a distance of 300 pc) at both sides of the VLA 2 YSO system, with an S-shape morphology, and are projected onto the east-west CO outflow. Most of them were resolved in smaller knotty substructures. The [Fe ii] emission only appears associated with HH 223. An additional nebular emission from the continuum in Hc and Kc appears associated with HH 223-K1, the structure closest to the VLA 2 YSO system, and could be tracing the cavity walls. Conclusions: We propose that the H2 structures form part of a large-scale near-infrared outflow, which is also associated with the VLA 2 YSO system. The current data do not allow us to discern which of the YSOs of VLA 2 is powering this large scale optical/near-infrared outflow. Based on observations made with LIRIS at the 4.2 m Williams Herschel Telescope operated at the Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias.Fits files of Table 1 are available at CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/523/A16