A right-wing uniformed group called the Italian National Guard was set up last month, likened by some to Benito Mussolini's Fascists. It vowed to start patrolling the streets.
But Interior Minister Roberto Maroni said the group, which sports beige uniforms and black military-style hats, would not be allowed to mount street patrols.
Mr Maroni, a member of the anti-immigration Northern League, has steered the legislation through parliament.
The party is a key ally of Italy's right-wing Prime Minister Silvio Berlusconi, and made tougher measures against immigration a condition of its support for his re-election last year.
The new law makes illegal immigration punishable by a fine of 5,000 to 10,000 euros (£4,276 - £8,553).
It also requires parents registering a birth to present documents proving that they are legal residents.
Opposition senators held signs calling the government "the real clandestines"
Italy has just introduced a policy of returning boatloads of migrants to Libya before they can claim asylum.
The government says it faces an unmanageable flood of immigrants, many arriving on outlying islands which do not have the means to cope.
More than 36,000 migrants landed on the shores of Italy last year - an increase of about 75% on the year before.
Critics say the government is targeting especially immigrants and Roma (Gypsies).
The Vatican said the new law was "focusing on crime and leaving integration completely out of the picture".
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