Five students were wounded and 27 arrested after police used batons to break up the anniversary rally, the Umma party of former premier Sadiq al-Mahdi said.
Five senior party officials were among those detained, politburo member Al-Wathiq al-Birair said.
He said the crackdown was sparked by the party's determination to mark the 20th anniversary of the overthrow of Jaafer Nimeiri's one-party regime in 1985, which ushered in a brief period of multi-party democracy before the 1989 coup that brought President Omar al-Beshir to power.
"The security authorities Tuesday night summoned Secretary General Abdel Nabi Ali Ahmed and ordered him not to organize the celebration in which other opposition parties were to take part," Birair said.
They "once again summoned the secretary general this morning (Wednesday) who told them that the celebration would be moved from the square (in the Omdurman area of the capital) to the party's headquarters.
"When the security officers told him that it should not be held anywhere, Ahmed insisted that the celebration must be organized because it is the party's right to commemorate the occasion.
"In late afternoon, students affiliated to the party gathered in front of the headquarters and, apparently in compliance with orders to prevent the celebration, riot police attacked the gathering, using teargas and batons, with the students throwing stones," said Birair.
"After sunset, the security men broke into the headquarters offices and arrested the secretary general, vice chairman Adam Mussa Madibbu and four other senior officials of the party," said Birair, adding that Madibbu was later released.
He said that while they were waiting outside party headquarters, party officials received "a notification from the registrar of political parties, Mohammed Ahmed Salim, saying that activities of the party would be suspended until it is registered officially."
One of Sudan's oldest political movements, ironically the Umma party led the way in seeking peace with the Khartoum regime. A breakaway faction led by a Mahdi relative even briefly joined the government.