The company, D'Alesio Group, said it had lost contact with the Montecristo after the attack at 6:45 am Italian time (0445 GMT) by five armed men about 620 miles off the Somali coast.
"The last we heard from the ship's command, the vessel had been attacked by a boat with five armed men on board," the company said in a statement.
The ship was carrying 23 people from Italy, India and Ukraine.
"Few of our men who escaped from the Tanzanian coast guard last week seized the ship," a pirate called Mohamed told Reuters by phone, referring to an incident last week when Tanzania's navy arrested pirates who tried to attack an oil exploration ship in its waters.
Somalia been mired in violence and awash with weapons since the overthrow of a dictator two decades ago, allowing piracy to flourish off the lawless nation's shores.
Preying on merchant vessels and pleasure boats, the pirates rake in tens of millions of dollars a year in ransoms.
"The ship is silent, and the engine is off," Andrew Mwangura, maritime editor of the Somalia Report and a former regional maritime official, told, confirming the Montecristo had been boarded by pirates.
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