Chad denies it aids JEM rebels, who operate close to the common border
Chad has closed its border with Sudan and suspended economic ties.
The move comes a day after Sudan cut diplomatic relations with Chad following a rebel attack near the Sudanese capital, Khartoum.
The Sudanese authorities accused Chad of helping a Darfur rebel group attack the city of Omdurman outside Khartoum - a charge Chad denies.
Earlier, Sudan released an opposition leader, Hassan al-Turabi, who had been accused of involvement in the attack.
The Darfur rebel group, the Justice and Equality Movement (Jem) attacked Omdurman, Khartoum's twin city across the River Nile, on Saturday.
The raid was the closest they had come to the capital in five years of conflict in Darfur.
The authorities are continuing to hunt for suspected rebels following the surprise attack.
On Monday a curfew was re-imposed in Omdurman and the BBC's Amber Henshaw in Khartoum says the atmosphere remains tense.
The government says it has repulsed the attack but Jem leader Khalil Ibrahim says the rebels will be back.
"This is just the start of a process and the end is the termination of this regime," he told Reuters news agency.
Sudan's ambassador to the UN, Abdalmahmood Abdalhaleem, told the BBC that captured rebels had identified Chadian officers killed during the assault.
Chad has denied any links with the rebel movement, as has Jem.
Experts say Chad and Sudan are fighting a proxy war using each other's rebels to achieve their military objectives.
The Chadian President, Idriss Deby, has blamed Sudan for supporting a Chadian rebel attempt on the presidential palace in the capital N'Djamena in February.
The move by Chad aims "to ensure the security of its territory and citizens and protect its economic and cultural interests" and to "guard against all surprises," a government statement said.
Sudan's Islamist leader Hassan al-Turabi was accused of having links to the rebels, and was detained on Monday and interrogated for several hours by the security forces over the attack.
He was freed from custody some hours later.
Mr Turabi has in the past denied such allegations, although some Darfur rebel leaders have followed him.
Mr Ibrahim used to follow Mr Turabi and correspondents say they share an Islamist outlook.
Mr Turabi was Sudan's main ideologue in the 1990s before falling out with President Omar al-Bashir. He has since been imprisoned several times.