Studies of the kinematics of NGC 1407 have revealed complex kinematical structure, consisting of the outer galaxy, an embedded disc within a radius of similar to 60 arcsec, and a kinematically decoupled core (KDC) with a radius of less than 30 arcsec. However, the size of the KDC and the amplitude of the kinematic misalignment it induces have not yet been determined. In this paper, we explore the properties of the KDC using observations from the Multi-Unit Spectroscopic Explorer (MUSE) Integral Field Spectrograph to map out the kinematics in the central arcminute of NGC 1407. Velocity and kinemetry maps of the galaxy reveal a twist of similar to 148 degrees in the central 10 arcsec of the galaxy, and the higher order moments of the kinematics reveal that within the same region, this slowly rotating galaxy displays no net rotation. Analysis of the stellar populations across the galaxy found no evidence of younger stellar populations in the region of the KDC, instead finding uniform age and super-solar a-enhancement across the galaxy, and a smoothly decreasing metallicity gradient with radius. We therefore conclude that NGC 1407 contains a triaxial, kiloparsec-scale KDC with distinct kinematics relative to the rest of the galaxy, and that is likely to have formed through either a major merger or a series of minor mergers early in the lifetime of the galaxy. With a radius of similar to 5 arcsec or similar to 0.6 kpc, NGC 1407 contains the smallest KDC mapped by MUSE to date in terms of both its physical and angular size.