Virginia Raggi said more arrivals could exacerbate social tension.
Her call follows local elections on Sunday in which the Five Star Movement performed poorly.
More than 500,000 people have arrived by boat since 2014. Nearly 200,000 are being housed in  centres across the country.
"We cannot permit the creation of more social tensions," Ms Raggi said on Facebook.
"That is why I am saying it is impossible, risky even, to think about creating any new reception structures."
The interior ministry has asked all Italian municipalities to find space for an expected 250,000 new migrants this year, up from about 180,000 last year.
Some observers say Ms Raggi is attempting to win back support by targeting migrants after her party failed to make the run-off in 24 of the main 25 cities choosing a new mayor.
About half of Italians do not want the country to take in more people, pollster Renato Mannheimer told Reuters news agency.
Italy is accommodating rising numbers of migrants because countries to the north have tightened their borders and some EU states have refused to take part in a plan to relocate 160,000 people from Italy and Greece.
Just over 20,000 migrants have so far been relocated under the plan and the EU has begun legal action against against Poland, Hungary and the Czech Republic for refusing to accept refugees.
An estimated 40% of the migrants in Italy have a valid claim to asylum or leave to remain on humanitarian grounds, AFP news agency reported.
The others are deemed to be illegal economic migrants and face deportation, but this can be difficult to arrange in practice because their countries of origin sometimes refuse to take them back.
A note on terminology: The BBC uses the term migrant to refer to all people on the move who have yet to complete the legal process of claiming asylum. This group includes people fleeing war-torn countries such as Syria, who are likely to be granted refugee status, as well as people who are seeking jobs and better lives, who governments are likely to rule are economic migrants.
The mayor of Rome, who is from the anti-establishment Five Star Movement, has asked Italy's government not to send more migrants to the city.