We used the Very Long Baseline Array and the European VLBI Network to perform phase-referenced very long baseline interferometry observations of the three most powerful maser transitions associated with the high-mass star-forming region G28.87+0.07: the 22.2GHz H_2_O, 6.7GHz CH_3_OH, and 1.665GHz OH lines. We also performed Very Large Array (VLA) observations of the radio continuum emission at 1.3 and 3.6cm and Subaru observations of the continuum emission at 24.5{mu}m. Two centimeter-continuum sources are detected and one of them (named hot molecular core (HMC)) is compact and placed at the center of the observed distribution of H_2_O, CH_3_OH, and OH masers. The bipolar distribution of line-of-sight velocities and the pattern of the proper motions suggest that the water masers are driven by a (proto)stellar jet interacting with the dense circumstellar gas. The same jet could both excite the centimeter-continuum source named HMC (interpreted as free-free emission from shocked gas) and power the molecular outflow observed at larger scales--although one cannot exclude that the free-free continuum is rather originating from a hypercompact H II region. At 24.5{mu}m, we identify two objects separated along the north-south direction, whose absolute positions agree with those of the two VLA continuum sources. We establish that ~90% of the luminosity of the region (~2x10^5^L_{sun}_) is coming from the radio source HMC, which confirms the existence of an embedded massive young stellar object exciting the masers and possibly still undergoing heavy accretion from the surrounding envelope.