In addition to the firing of Oleksandr Zatynayko and Petro Shulyak, Kuchma also reprimanded his Defense Minister Evhen Marchuk responsible for the incident, the president's press service said.
A government committee had recommended the measures last week.
The explosions occurred on May 6 after a fire erupted at a military base near the southeastern town of Melitopol.
Six Ukrainian soldiers, including the commander of the military base, have been charged over the explosions, which lasted nearly a week and forced 7,000 people to flee their homes.
Two are accused of starting the fire that triggered the blasts.
The equivalent of 900 wagon-loads of ammunition were destroyed by the flames, causing losses to the state of 2.25 billion hryvnas (353 million euros, 422 million dollars).