The Sudanese government imposed curfew in Khartoum from 6:00 p. m. on Monday (1500 GMT) to 6:00 a.m. (0300 GMT) on Tuesday.
An eyewitness said the streets in Khartoum were almost empty except the security forces were deployed.
Riots broke out in the streets of Khartoum after Garang was confirmed dead in a helicopter crash on his way back from Uganda to southern Sudan Saturday night.
A group of people, most of them thought to be southerners, took to the streets in central Khartoum to express their shocked feelings toward the tragedy.
The rally stirred disorder, with some of the rioters smashing cars and looting and setting ablaze shops where black smoke was seen rising.
A security source said at least 24 people were killed in clash with police.
Earlier in the day, Sudanese President Omar el-Bashir announced Garang's death, adding it was a great loss to the Sudanese people.
Bashir urged all Sudanese people to keep calm and stick to unity and stability in the country.
Garang, who led the former southern rebel group Sudan People's Liberation Movement, signed a peace deal with Bashir on Jan. 9 to end a 21-year civil war in the south.
Under the power-sharing deal, he was sworn in as first vice president of the national unity government on July 9 in Khartoum.