A convoy of 20 heavily armed vehicles entered Machar's residence in the capital Juba and took him away, according to a statement from Machar's party.
"His bodyguards were disarmed and an arrest warrant was handed over to him on unclear charges. Efforts are currently being made to locate him," writes Reath Muoch Tang, chairman of the party's foreign affairs committee in a statement.
The UN peacekeeping forces in South Sudan, UNMISS, said on Thursday that reports of the arrest constitute a dangerous escalation in the conflict between the two rival leaders.
"This evening, the country's leaders are on the brink of falling back into a comprehensive conflict," says the head of the UN mission Nicholas Haysom in a statement.
The two camps have previously fought a five-year-long civil war that led to a fragile peace agreement between Kiir and Machar in 2018.
Violations of the peace agreement risk "not only destroying South Sudan but also affecting the entire region," adds Haysom.