The system of galaxies around NGC\,4490 was recently highlighted to display a flattened, kinematically correlated structure reminiscent of planes of satellite galaxies around other hosts. Since known satellite planes are in tension with expectations from cosmological simulations in the Lambda Cold Dark Matter (Lambda CDM) model, we aim to quantitatively assess for the first time the tension posed by the NGC\,4490 system. We measured the on-sky flattening as the major-to-minor axis ratio $b/a$\ of the satellite distribution and their line-of-sight kinematic correlation. Analogs to the system were selected in the TNG50 simulation and their flattening and correlation were similarly measured. We confirm the strong kinematic coherence of all 12 observed satellite objects with available line-of-sight velocities (of 14 in total): the northern ones approach and the southern ones recede relative to the host. The spatial distribution of all 14 objects is substantially flattened with $b/a = 0.38$\ (0.26 considering only the 12 objects with available velocities). Such extreme arrangements are rare in the Lambda CDM simulation, at a level of 0.21 to 0.35<!PCT!>. This fraction of analogs would drop further if at least one of the two satellite objects without velocities is confirmed to follow the kinematic trend, and would become zero if both are rejected as non-members. We also identify a likely galaxy pair in the observed system, and find a similar pair in the best-matching simulated analog. Our measurements establish NGC\,4490 as another strong example of a satellite plane in the Local Volume. This emphasizes that planes of satellites are a more general issue faced by Lambda CDM also beyond the Local Group. The tension with typical systems drawn from simulations suggests that the observed one requires a specific formation scenario, potentially connected to the larger-scale galaxy alignment in its vicinity. The presence of galaxy pairs in the observed and a simulated system hints at the importance such groupings may have to understand satellite planes.