In this paper, the problem of Hermite interpolation by clamped Minkowski Pythagorean hodograph (MPH) B-spline curves is considered. Using the properties of B-splines, our intention is to use the MPH curves of degrees lower than in algorithms designed before. Special attention is devoted to C1∕C2 Hermite interpolation by MPH B-spline cubics/quintics. The resulting interpolants are obtained by exploiting properties of B-spline basis functions and via solving special quadratic and linear equations in Clifford algebra Cℓ2,1. All the presented algorithms are purely symbolic. The results are confirmed by several applications, in particular we use them to generate an approximate conversion of a given analytic curve to MPH B-spline curve with a high order of approximation, then to an efficient approximation of the medial axis transform of a planar domain leading to NURBS representation of the (trimmed) offsets of the domain boundaries, and to skinning of systems of circles in plane.