Stewards fined the 20-year-old, who is a development driver for the U.S.-owned Haas Formula One team, 66,000 euros (£58,216.05) and disqualified him from Sunday's race at Silverstone.
He was banned from the next two rounds in Hungary and Belgium, four races in all.
Formula Two is an official feeder series for Formula One, with races run after Saturday qualifying and before Sunday's grand prix.
Race organisers said Ferrucci had deliberately driven into the rear of Trident team mate Arjun Maini's car on the cooldown lap. He also forced Maini off the road during the race.
The Formula Two website (www.fiaformula2.com) said the American had also been seen in the car, while it was going from the support paddock to pitlane, "wearing just one glove and holding a phone in his hand".
It said that "violated both the technical and sporting regulations for incorrect driver safety equipment and the prohibition of wireless transmission devices within the car."
Trident apologised on Twitter for their driver's "unsportsmanlike and above all uncivilized behaviour".
"The contractual implications of what has happened will be dealt with by our lawyers," they added. "Never in these 12 years of sporting activity has anything even close to this ever occurred."
(Reporting by Alan Baldwin, editing by; Neil Robinson)
