We study the non-monotonic Keplerian velocity profiles related to locally non-rotating frames (LNRF) in the field of near-extreme braneworld Kerr black holes and naked singularities in which the non-local gravitational effects of the bulk are representedby a braneworld tidal charge b and the 4D geometry of the spacetime structure is governed by the Kerr-Newman geometry. We show that positive tidal charge has a tendency to restrict the values of the black hole dimensionless spin a admitting the existence of the non-monotonic Keplerian LNRF-velocity profiles; the non-monotonic profiles exist in the black hole spacetimes with tidal charge smaller than b = 0.410 05 (and spin larger than a = 0.768 08). With decreasing value of the tidal charge (which neednot be only positive), both the region of spin allowing the non-monotonicity in the LNRF-velocity profile around braneworld Kerr black hole and the velocity difference in the minimum-maximum parts of the velocity profile increase implying