"We think Israel did the bombing," Culture and Information Minister Ahmed Bilal Osman told a news conference. "We reserve the right to react at a place and time we choose."
The military and foreign ministry in Israel, which has long accused Khartoum of serving as a base for militants from the Palestinian Islamist group Hamas, refused to comment.
Osman said four radar-evading aircraft conducted an attack at around midnight (2100 GMT) on the Yarmouk military manufacturing facility in the south of the Sudanese capital.
Evidence pointing to Israel was found among remnants of the explosives, he said, adding that the cabinet would hold an urgent meeting at 8:00 pm.