The SPLM is concerned that southern Sudanese now living in the north could be less supportive of a campaign for independence.
Badriya Suleiman, the chair of the parliament's justice committee, said barring southerners from voting outside their region would be a violation of Sudan's temporary constitution.
"The article was changed because it violated the transitional constitution that gives Sudanese freedom of movement from one area to the other," she told reporters.
Peace deal 'violated'
But Yasser Arman, the SPLM deputy secretary general, called the vote a breach of the 2005 power-sharing accord that ended decades of civil war that had caused the deaths of millions of people.
"What happened today is the worst violation against the Comprehensive Peace Agreement, and from today we will not participate in parliamentary sessions until this matter is resolved," he said.
South Sudan secured the independence vote, due to be held in 2011, as part of the peace accord.
Analysts had warned of a risk of a return to conflict if the parties could not agree terms for the laws, whicch also pave the way to national elections, due in April 2010.
A key point of disagreement was the organisation of the democratic process under the results of a recent census are scheduled to be the basis for electoral constituencies for the 2011 vote.
The government in Khartoum released the census last May showing that more than 500,000 southerners live in the north, though southern regional officials have disputed that figure.
The national vote will be the first in Sudan since 1986, three years before Omar Hasan al-Bashir, Sudan's president, toppled a democratically elected government in a bloodless military coup.
Relations between the SPLM and al-Bashir's NCP have been strained, most recently when authorities in Khartoum arrested two senior SPLM officials and scores of their supporters during a protest earlier this month.