Fire engulfed the Yarmouk plant and nearby buildings after the explosion, but no deaths were reported.
Culture and Information Minister Ahmed Belal Osman said four Israeli planes had attacked the factory. Israel would not comment on the accusation.
“We think Israel did the bombing,” Osman said. “Four military planes attacked the Yarmouk plant.” he said, adding that the planes appeared to come from the east, Reuters news agency reported.
“We reserve the right to react at a place and time we choose.”
A spokesman for the Israeli army, Avikhai Adraie, told the BBC’s Arabic service that Israel had no comment on the accusation.
It’s hardly the first time that Sudan has blamed Israel for such attacks.
In April 2011, Khartoum held Tel Aviv responsible for an air strike that killed two people in a car near the city of Port Sudan. Israel did not comment on that incident.
The Jewish nation was also blamed for a strike on a convoy in northeastern Sudan in 2009, but has neither confirmed nor denied its involvement.
At this stage, there is no way of knowing for certain who was responsible for the air attack against the Yarmouk arms factory in Khartoum.
While the Sudanese authorities are yet to provide any evidence for their accusation that it was Israel, this is by no means as outlandish as it might sound. For a bitter secret war has been going on for a number of years between Israel and Hamas, with Sudan apparently very much one of the battlegrounds.
United States diplomatic cables have revealed alleged arms smuggling networks running through Sudan. In January and February of 2009, there were two mystery air attacks on convoys in the Sudanese desert. More recently, in April last year, there were reports that a senior Hamas figure, thought to be responsible for arranging arms supplies, was killed near Port Sudan.
The Sudanese government accused Israeli attack helicopters of destroying the car in which two individuals were travelling.
Armed forces spokesman Col al-Sawarmi Khalid said the explosion set light to surrounding grass and trees, sending flames over a wide area, state news agency Suna reported.
He said civil defense forces had contained the fire and that investigations were under way “to determine the causes of the explosion as well as assessing human and material loss”.
Witnesses reported seeing two or three fires with dense smoke and intermittent flashes of white light.
Earlier, Khartoum governor Abdul Rahman al-Khidir told local TV that the explosion had occurred at midnight and that a preliminary investigation suggested it had happened in a store room.
Some people had been taken to hospitals suffering from the effects of smoke inhalation but otherwise there were no casualties, said Mr Khidir.
In 1998, the U.S. launched a missile attack on a pharmaceutical plant in Khartoum, alleging that it was making materials for chemical weapons.
Sudan denied the allegation, insisting that then-U.S. President Bill Clinton had attacked a factory that manufactured anti-malaria medicines and veterinary products in defiance of international laws.