The plane, flying from Bologna to Paris, landed at Lyon in France where the man surrendered and passengers were freed unharmed, the national police service told BBC News Online.
It later emerged the man had a history of hijackings, raising questions about how he had managed to secure a seat on the plane.
Fifty-seven passengers and seven crew were on the MD-80 plane, flight AZ364/AF9851, Alitalia said in a statement.
No-one was injured during the incident.
Recent hijack scares
22 November: A passenger on an Air France flight from Montreal to Paris is arrested, suspected of planning a hijack attempt
18 November: An Arab Israeli man attempts to break into the cockpit of an El Al flight from Israel to Turkey
15 October: A passenger with a pistol tries unsuccessfully to take over a flight from Sudan to Saudi Arabia
The plane was hijacked while flying over Swiss airspace, say police.
Italian authorities say they have identified the man as a former policeman, thought to be aged around 30 .
They say that three years ago he attempted unsuccessfully to hijack a Moroccan airliner flying from Marseille to Paris and on another occasion he tried to hijack a high-speed train in Italy, breaking into the driver's compartment, the BBC's Rome correspondent David Willey reports.
The man's mother, on learning that her son had hijacked a plane, reacted by saying: "My God, he's done it again!", said Italian newspaper La Repubblica website.
Cockpit threat
The drama began shortly after take-off.
"A man got up from his seat, went to the middle of the aircraft and, holding a small box, shouted: I'm a terrorist, I belong to al-Qaeda, and I'm going to blow up the aircraft," La Chaine Info (LCI) TV channel reported.
Police do not believe the man was armed.
"He was carrying a remote control device which he said was linked to a bomb," spokesman Gerard Laurent told BBC News Online.
"He went into the cockpit and threatened the pilot. He said he wanted to speak to the press, and said he was a member of al-Qaeda."
At that point, the pilot called the control tower and it was decided to divert the plane to Lyon, the nearest French airport, LCI said.
Special police units were called to the scene, said Mr Laurent, and arrested the man when he surrendered.
Passengers
The plane was bound for Paris Roissy-Charles de Gaulle airport.
Most of the passengers were allowed to get off the plane at Lyon's Saint-Exupery airport, shortly after landing.
The plane had taxied to the end of a runway.
Alitalia confirmed in a statement that an attempt to hijack the plane had been foiled.
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