The move came amid a wave of violent protests against Barzani in southern opposition strongholds which Barzani's Kurdish Democratic Party accuses Gorran of fomenting.
The autonomous region's parliament speaker and ministers from the Gorran party were asked by the KDP to leave the city, a statement said.
"The KDP politburo used its representatives in parliament and government to inform the president of parliament and the Gorran ministerial team that they must not attend their places of work and must leave our regional capital," Gorran's statement said.
Gorran (Movement for Change) is the second largest bloc in parliament.
At least four people were killed on Saturday and Sunday in a string of protests that spread to most major towns in the south of the autonomous region in recent days.
The demonstrations started in Sulaimaniyah, the main city in southern Kurdistan and a traditional bastion of opposition to the KDP, to demand payment of overdue salaries for civil servants.
They evolved into protests calling on Barzani, whose mandate expired in August, to step down.
Several local KDP headquarter buildings were set on fire by the protesters.
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"I condemn the recent violence and mourn loss of innocent lives. This was a deliberate plan by Gorran activists to incite hatred and violence," said Masrour Barzani, the region's intelligence chief and also the president's son.
The 69-year-old has headed the KDP, one of the two historical Iraqi Kurdish parties, since 1979 and been president of the autonomous region since 2005.
The prime minister of the autonomous region is Barzani's nephew, Nechirvan Barzani.
On Saturday, the Arbil staff of Sulaimaniyah-based TV station NRT was detained and driven from the region of the capital by security forces loyal to the KDP.
The channel said in a statement that its office in Dohuk, the other major city in Kurdistan -- located in the west of the region and also under KDP control -- was also shut down.
"NRT asks the representatives of foreign countries in Kurdistan, all organisations and political parties, and the people of Kurdistan to raise their voices against these abuses," it said.
Barzani has been accused by critics of amassing huge wealth for his family instead of serving the population.
He served two terms and the two-year extension Kurdish parties agreed to in 2013, which expired on August 19, leaving the region in an institutional vacuum.
Barzani wants to stay on, arguing that his leadership is required to steer the region as its peshmerga forces play a significant role in battling the Islamic State group.