The Palau-flagged tanker Elhiblu I picked up the migrants on Tuesday evening in international waters where Libyan coastguards are responsible and then headed back to Tripoli.
But six nautical miles from port the ship suddenly changed course heading for the north, and was on Thursday evening halfway between Tripoli and Malta, according to Salvini.
"They're not shipwrecked, they're pirates!" Salvini tweeted, promising that they would not be allowed to disembark in Italy.
The Libyan authorities and the ship's operator in Tripoli were not immediately available for comment.
Migrants in chaos-wracked Libya face trafficking, kidnap, torture and rape, according to the United Nations and aid groups.
Following Rome's increasingly tough anti-migrant stance, boats that pick up migrants making the perilous journey across the Mediterranean increasingly return them to Libya.
Boatloads of rescued migrants have in recent months refused to disembark in Libya, prompting the authorities there to use force.
Migrant arrivals from North Africa and the Middle East have been sharply reduced since a 2015 peak when Europe faced its worst migration crisis since World War II.