Following up on a faint detection of a near-infrared ( NIR ) source at the position of the X-ray thermal isolated neutron star RX J0806.4–4123 , we present new Hubble Space Telescope ( HST ) observations in the H -band . The NIR source is unambiguously detected with a Vega magnitude of 23.7 \pm 0.2 ( flux density of 0.40 \pm 0.06 \mu Jy at \lambda = 1.54 \mu m ) . The source position is coincident with the neutron star position , and the implied NIR flux is strongly in excess of what one would expect from an extrapolation of the optical-UV spectrum of RX J0806.4–4123 . The NIR source is extended with a size of at least 0 \farcs { 8 } and shows some asymmetry . The conservative upper limit on the flux contribution of a point source is 50 % . Emission from gas and dust in the ambient diffuse interstellar medium can be excluded as cause for the extended emission . The source parameters are consistent with an interpretation as either the first NIR-only detected pulsar wind nebula or the first resolved disk around an isolated neutron star .