Critics say it would strip Italy of vital democratic checks and balances put in place after World War II
The prime minister has bet his political career on the reform, which would dramatically reduce the powers of the upper house of parliament, but is set to lose the December 4 vote according to the latest polls.
Massimo Bottura, whose Osteria Francescana in Modena was named the world's best restaurant this year, said in an interview on the Corriere della Sera website that he might leave the country if the reform is defeated.
"If the 'No' wins I'll be tempted to abandon everything and move abroad. I'll thank my country, which has given me so much, I'll close up shop and re-open in New York," said Bottura, whose restaurant has three Michelin stars.
He blamed low morale in a country where the prevalent opinion was "it can't be done in Italy".
"If that logic wins, it's over," he said.
Over 80 well-known figures also signed a petition calling for support for the "Yes" camp, including World Cup-winning footballer Marco Tardelli and Turkish-Italian film director Ferzan Ozpetek.
The proposed constitutional reform is considered by supporters to be the most important in the eurozone country since World War II.
It is aimed at increasing political stability in a country which has had 60 governments since 1946, by streamlining parliament and the electoral system.
But critics say it would strip Italy of vital democratic checks and balances put in place after World War II.
The referendum has become a vote of confidence in the centre-left prime minister who took office in early 2014 and experts say the fate of his administration hinges on the outcome.