The curfew in the capital was due to start at 6pm, the official Sudan News Agency (Suna) reported.
Earlier on Monday thousands of southern Sudanese wielding knives and bars looted shops and clashed with police in the capital's streets after learning of the death of ex-rebel leader and First Vice-President Garang.
Twenty-four people, including some police officers, were killed, a police official said.
"People have been running all over the streets. The policemen are taking people from the streets. There is fire and smoke," a witness said on Monday.
"They are beating anybody who looks like Arab," said Swayd Abdullah, a student.
Shops closed and there was a heightened security presence in the streets, witnesses said.
The southern Sudanese, who recently gave Garang a tumultuous welcome when he travelled north to take up his post as vice-president in the new power-sharing government, smashed cars and shops in several hours of rioting, the witnesses said.
Some gunfire could be heard, although it was not clear whether that was in mourning for Garang or from fighting.
Clashes in south
There were reports of violence in the south, where Garang's Sudan People's Liberation Movement (SPLM) fought a 21-year war against the mainly Islamic government in Khartoum until January's peace accord.
John Garang became vice-
president after a peace accord
An aid worker with Catholic Relief Services in Yai, in southern Sudan, said there was shooting there but only out of respect for Garang.
"People are shooting in the air as a sign of mourning. There are gunshots everywhere," he told Reuters in Nairobi by phone from Yai.
The SPLM named Garang's longtime deputy, Salva Kiir, as the late leader's successor, Aljazeera learned.
"The SPLM leadership and the SPLA military command affirmed General Salva Kiir as the chairman of the SPLM and commander-in-chief of the SPLA," the movement said in a statement after a meeting on Monday.
"I call upon all members of the SPLM and the entire Sudanese nation to remain calm and vigilant," Kiir said in Nairobi, Kenya, adding that he was on his way to an emergency meeting he had called of the SPLM's top decision-making body. Kiir later flew to Sudan.
Kiir was also named to succeed Garang as president of south Sudan, Garang spokesman Yasser Arman said in Nairobi.
Arman indicated that Kiir would also take Garang's post as first vice-president in the national government, but there was no immediate confirmation from Khartoum.
In Nairobi on Monday, wailing mourners gathered outside his movement's headquarters.
Successor Salva Kiir (R, in grey)
and relatives with Garang's coffin
Groups of southern Sudanese men huddled on Nairobi's main street, Kenyatta Avenue, discussing Garang's death.
Atem Maper, 30, said that younger exiles were suspicious of the circumstances surrounding Garang's death.
"People are worried that the war will continue," Maper said. "They didn't understand the way he died. We are going to see."
Key to peace
Kenyan President Mwai Kibaki said Garang had been key to the peace, but expressed "hope and optimism that every effort will be taken to ensure that the physical absence of Dr Garang will not in any way jeopardise the gains made towards durable peace."
Kibaki ordered the Kenyan flag flown at half staff for the next three days in honour of Garang, whom he praised as patient, energetic and skilled negotiator ready to make
The chief mediator during the negotiations that ended 21 years of war, retired Kenyan General Lazaro Sumbeiywo, said Garang's death could hurt the January peace agreement, but he said that he was confident Sudan's leaders could overcome this, particularly with the support of the international community.
Kenya's Mwai Kibaki hopes the
death will not jeopardise peace
"The agreement will suffer," Sumbeiywo said. "It will suffer because of the person of John. Dr John Garang was a special person. He was a very focussed, very solid man, who knew exactly what he wanted for the Sudan."
Ahmad Aboul Gheit, Egypt's foreign minister, called on all parties in Sudan to pursue the peace "Garang was working toward."
Jordanian Deputy Prime Minister Marwan al-Muasher expressed Jordan's condolences.
Arabs, particularly neighbouring Egypt, had closely watched the Sudanese peace process, fearful of the possibility that an Arab neighbour could be split.
John Duom, 67, an SPLM official who had known Garang since childhood, compared him to Moses.
"He has shown us the direction to follow," said Duom, wiping tears from his eyes. "We wish God had spared his life until after six years, after the referendum."
The United States has dispatched two senior envoys to Sudan in hopes of keeping the peace process in the African state on track.