The restriction was imposed by the European Union, but under United Nations rules, heads of state are allowed access to all UN conferences.
The heads of state and ministers attending the four-day meeting are expected to commit themselves to further efforts to reduce the number of hungry people worldwide.
Opposition leaders in Zimbabwe have expressed anger that Mr Mugabe is apparently being allowed to take part when, they say, he is responsible for causing starvation in his own country.
The summit takes place against the background of a worsening food crisis in southern Africa, including Zimbabwe.
An estimated 12.8 million people in six countries are at risk of starvation because of drought, floods, government mismanagement and economic instability.
Colonial legacy
"It is ironic and laughable that a person who has masterminded the impoverishment of the country and the mass starvation of children ... will have the gall to go to a food conference", Welshman Ncube, Secretary-General of Zimbabwe's opposition Movement for Democratic Change told The Times newspaper of London.
According to some reports, Mr Mugabe is expected to strongly attack the legacy of colonialism and meet UN Secretary-General Kofi Annan when he attends sessions on Monday and Tuesday.
There has been no official comment from the Italian Government on the anticipated arrival of Mr Mugabe and other Zimbabwean ministers.
Last month, Mr Mugabe attended the world children's summit in New York, despite a travel ban imposed by the United States as part of international sanctions against the Zimbabwean leader and senior officials.
In April, the head of Zimbabwe's police force was allowed to visit France, again despite a ban on travel.
Emergency measures
According to a study by UN agencies last month, Zimbabwe's maize harvest this year is expected to be slightly more than 500,000 tonnes - just over a quarter of the average crop produced in the last decade.
The shortfall is already being felt in urban and remote rural areas.
The government has declared a state of disaster as worsening shortages threaten widespread famine.
It has blamed the crisis on a drought, but the World Food Programme says agricultural disruption caused by the confiscation of white-owned farms has also contributed to the problem.