First investigations of ferromagnetic (Ga,Mn)As/GaAs Esaki diodes under hydrostatic pressure were performed. The I\(V) characteristics had bi-exponential character with two excess current regions related to impurity-assisted tunneling, which concealed band-to-band tunneling, resolved only in the logarithmic derivative of current upon bias. A decrease of tunneling current was observed under pressure. This is understood as a combined effect of the increase of the energy gap with pressure and a possible decrease of density of states in the forbidden gap. Tunneling anisotropic magnetocurrent (TAMI) showed nonmonotonic bias dependence, which stays in a reasonable agreement with the theory by Sankowski (2007). The overall character of the TAMI did not change with pressure, however, at negative bias an increase of TAMI was observed and at positive bias the minimum became shallower. The magnetic anisotropy of (Ga,Mn)As valence band subbands seems unaltered by hydrostatic pressure, but more in-depth description of TAMI is necessary to explain the observed pressure variation. (C) 2016 Elsevier B.V. All rights reserved.