In order to explore a minimal momentum uncertainty principle in Heisenberg's uncertainty principle, the minimal momentum uncertainty principle (MMUP) was proposed. The correction on the canonical commutation relation of MMUP can be parametrized by a and alpha'. In the macroscopic scale, MMUP could change bodies' orbital motion, which is different from the results of general relativity ( GR). In the present work, we mainly focus on the influence of MMUP on the tests of the Solar System and the binary pulsars. In the Solar System, the perihelion shift of a planet has been remodeled under MMUP by the data of INPOP10a, EPM2011 and INPOP15a. In five systems of binary pulsars, the upper bounds of a and alpha' are obtained by using the data of the secular periastron precessions. These five systems are PSR B1913+16, PSR B1534+12, PSR J1756-2251, PSR B2127+11C and PSR J0737-3039. Few studies about the tests have been done before and the effects of MMUP on these systems are investigated for the first time. They show that the upper bounds of a and a alpha' constrained by planets of the Solar System and the binary pulsars are alpha + alpha'= 10- 28 similar to 10(-36) m(-2), tighter than the previous result by at least 2 orders of magnitude. It is expected that the bounds on MMUP will be further improved by tremendous advances in techniques for deep space exploration and by new tracking data sets. Copyright (C) EPLA, 2018.