The request was made public on Tuesday, after 5-Star took a drubbing at local elections on Sunday, failing to make the run-off in 24 of the main 25 cities called to pick a mayor. A national vote is due by the first half of next year.
Managing newly arrived migrants has become one of the thorniest issues for Italy's government, which is run by the Democratic Party (PD), the 5-Star's rival.
More than half a million people have arrived by boat from North Africa since 2014, and almost 200,000 are being housed in state-funded centres while they put forward asylum requests.
Raggi wrote to the interior ministry, which is responsible for plans to relocate asylum seekers from arrival points on the southern coasts to the rest of the country, asking to suspend further arrivals to the capital, her spokesman said.
"This administration hopes the decisions about where to put new centres will take into account the evident pressure migration is putting on Rome, and the consequences which may be devastating socially and for the protection of the people they are built for," Raggi said in the letter.