We report a faint nonaxisymmetric structure in NGC 1087 through the use of James Webb Space Telescope Near Infrared Camera, with an associated kinematic counterpart observed as an oval distortion in the stellar velocity map, Hα, and CO J = 2 → 1 velocity fields. This structure is not evident in the MUSE optical continuum images but only revealed in the near-IR with the F200W and F300M band filters at 2 μm and 3 μm, respectively. Due to its elongation, this structure resembles a stellar bar although with remarkable differences with respect to conventional stellar bars. Most of the near-IR emission is concentrated within 6″∼500 pc with a maximum extension up to 1.2 kpc. The spatial extension of the large-scale noncircular motions is coincident with the bar, which undoubtedly confirms the presence of a nonaxisymmetric perturbation in the potential of NGC 1087. The oval distortion is enhanced in CO due to its dynamically cold nature rather than in Hα. We found that the kinematics in all phases, including stellar, ionized, and molecular, can be described simultaneously by a model containing a bisymmetric perturbation; however, we find that an inflow model of gas along the bar major axis is also likely. Furthermore, the molecular mass inflow rate associated can explain the observed star-formation rate in the bar. This reinforces the idea that bars are mechanisms for transporting gas and triggering star formation. This work contributes to our understanding of nonaxisymmetry in galaxies using the most sophisticated data so far.