"There has been no contact with the ship since 6:44 am (0444 GMT)," when the captain sent a message saying the vessel was under attack and he had activated "the security operating procedure", the company said.
"After 10 hours without news, we can consider the ship hijacked," a spokesman from the Livorno-based company told AFP.
There are six Indians, seven Italians and 10 Ukrainian nationals aboard the ship, which was travelling from Liverpool to Vietnam with a cargo of scrap iron, according to Italian media reports.
Commander Harrie Harrison, spokesman of the EU counter-piracy mission, told AFP that warships and aircraft would search for the missing ship.
"We will investigate as soon as we are able to get an asset in the area to see if we can locate the ship," he said.
The ship was being escorted by a Japanese military vessel, according to the Repubblica newspaper, which said NATO's maritime task force was dispatching a vessel to the scene.
The owners of the M/V Montecristo said they were "actively collaborating with all the related Italian and international authorities to respond to the emergency".
Italy's foreign ministry said it was closely monitoring the situation.