A key obstacle in the search for new non-equilibrium phases of matter, is the tendency of closed quantum many-body systems to indefinitely absorb energy from a time-periodic driving field. A promising solution is the addition of strong disorder, which can suppress energy absorption in these systems by causing them to enter the many-body localized (MBL) phase. Here we propose the use of a specific driving field to stabilize non-equilibrium phases, utilizing merely a weak static disorder. Applying an AC-electric field to a 1D system of weakly disordered interacting hardcore bosons leads to a suppression of the effective static hopping amplitude, through the phenomenon of coherent suppression of tunneling. The suppression of the hopping amplitude increases the relative strength of disorder, causing the system to enter the MBL phase. Using numerical simulations, we find the transition into the MBL phase above a critical driving frequency and in a range of driving amplitudes.