Ibrahim said that a number of Sudanese army troops and one of his own commanders had died in the hour-long attack. He said that oil workers had deserted the scene.
The oilfield is in the Kordofan region, which neighbours Darfur and has large energy reserves.
But the Sudanese military official said that none of the country's oil facilities were under JEM control and "the security of oil infrastructure has been preserved".
He added that about 20 rebels had attacked an army camp near an oil refinery but only stole a Chinese oil company's vehicle before dispersing when they were confronted.
Ibrahim said that the move was part of an ongoing campaign to force Chinese oil firms out of Sudan, and that more attacks would follow possibly within the next few days.
Government arms and artillery had also been seized, he said.
The companies have been targeted as the rebels accuse them of helping to fund the Khartoum government through oil revenues and supplying the army with weapons.
The oilfield is run by the Great Wall Oil Company of China, which produces about 35,000 barrels of oil a day at the facility.
JEM previously attacked the company on October 23, kidnapping five oil workers, according to one of the group's commander.