Hundreds of opposition protesters gathered despite their rally being banned
Protesters set alight the office of Sudan President Omar al-Bashir's party in a southern town after three southern politicians were arrested in Khartoum.
There were no reports of casualties at the National Congress Party (NCP) building in Wau, and police later freed the three politicians.
The SPLM joined the government in 2005, ending a 22-year north-south conflict.
But tensions between the SPLM and their power-sharing partner the NCP have been rising ahead of next year's elections.
'We want freedom'
The vote will be the first presidential, parliamentary and local elections in 24 years.
James Copnall, BBC News, Khartoum
The latest demonstration of the mistrust between the SPLM and the NCP was certainly vivid, even if the SPLM leaders were released within hours.
What it illustrates clearly is the widening gulf between the sides. The NCP seems unwilling to allow its opponents to take to the streets. The SPLM and its northern allies knew the probable consequences of their actions once the police had declared the rally illegal.
But with time running out before next April's elections, both sides seem less and less willing to compromise. The clampdown on the protesters may also cement a loose alliance between the SPLM and various northern opposition parties into something more concrete.
Monday is the final day for voters to register for the election, and the government declared it a public holiday in an effort to encourage a good turnout.
But the SPLM and the NCP have failed to agree on changes to the election laws.
And about 20 opposition parties called for a gathering in front of the parliament building in the capital to demand electoral reform.
Hundreds of demonstrators turned out, watched by lines of armed police.
The AFP news agency reported that demonstrators marched through Khartoum and its neighbouring city Omdurman waving placards and chanting: "We want our freedom."
As the protest grew - with some reports estimating thousands of people had joined the rally - police fired tear gas and beat the protesters with batons.
SPLM secretary general Pagan Amum was arrested along with his deputy Yasir Arman and Abbas Gumma, a state minister in the interior ministry.
Reports said dozens of other protesters were detained.
Mr Arman told a news conference that he had been beaten while in custody. SPLM leaders condemned the crackdown and vowed to continue protesting.
Following the arrests, angry crowds attacked an NPC office in Wau and torched it.
Earlier reports stated that the NPC office in another southern town, Rumbek, had been burnt - but southern President Salva Kiir denied the claims.
After the crackdown, SPLM members accused the NCP of suppressing free speech.
Pagan Amum and his deputy were among those arrested by police
But interior ministry officials said the protest was outlawed because the organisers had failed to apply for permission to hold the event.
Analysts say the argument over electoral laws and the crackdown on protesters show a deteriorating relationship between the NCP and its detractors.
A 22-year war between the mainly Muslim north and the Christian and animist south claimed the lives of some 1.5 million people.
Semi-autonomous southern Sudan has been controlled by the SPLM since a peace deal in 2005 ended the civil war.
A referendum on whether the south should secede is due in 2011.