The Soviet-era Antonov aircraft had landed within seconds of each other when the accident occurred, an airport official said.
“Eight people were injured and taken to hospital when two military planes collided at Khartoum airport,” said another official who spoke to AFP on condition of anonymity.
The Sudanese military is expected to comment on the accident later on Wednesday.
Video footage posted on social media showed two planes moving along the runway before one suddenly rams the tail of the other.
Both planes appeared to have been badly damaged in pictures posted online.
Airport officials said the facility had been temporarily closed after the accident.
Wednesday’s accident is the third to have hit Sudan’s ageing military fleet in less than a month.
On September 21, two pilots were killed when their military jet crashed near Omdurman, the twin city of Khartoum on the west bank of the Nile.
It came days after a military helicopter crashed on landing in Darfur. All passengers were rescued as the helicopter caught fire.
Most of Sudan’s fleet consists of Russian-made aircraft, and in recent years it has suffered several crashes, with the military frequently blaming technical problems and bad weather.