"The crash took place at 13:45 Moscow time [10:45 GMT]," the spokesman said, adding that the plane had hit the ground 38 km (23.6 miles) to the southeast of the city. No damage has been reported.
Shortly after the crash, Colonel Vladimir Drik, the official spokesperson for the Russian Air Force, announced that Su-24M flights had been temporarily suspended until "the cause of the incident near Voronezh is established."
A source in the Russian Defense Ministry said that according to preliminary information the crash was caused by a malfunction in the plane's flight control system, after which the pilots decided to eject.
The Su-24 is a two-seat, twin-engine tactical bomber similar to NATO's Tornado and Mirage 2000 planes.
The plane has been in service with the Russian Air Force since the mid-1970s. However, in recent years Russia has gradually been phasing out the planes, which have a patchy safety record.
According to the Defense Ministry, the Su-24 will be gradually replaced with new Su-34 Fullback strike aircraft, which has the potential to become the top plane in its class for years to come.