It says the Boeing 757 aircraft was forced to return to Cheddi Jagan International Airport minutes after departing for Canada because of technical difficulties and overran the airstrip.
A Fly Jamaica Airways Boeing Co. jet en route to Toronto crash landed after returning to Guyana with a fault.
Those injured are in non-life-threatening condition and being treated in hospital.
"Everyone was going insane, screaming, crying for their lives, everything", said passenger Invor Bedessee, describing how some people were injured getting off the flight.
Minister Patterson explained that the flight departed the airport at 02:10hrs and at about 02:21grs, the Pilot indicated that he was experiencing hydraulic problems.
Fly Jamaica Flight 256 headed back to the Guyanan capital Georgetown because of a technical problem, the airline said in a statement on its website, adding that it believes all 118 passengers and 8 crew members are safe.More news: Klopp: I can’t count the ways it went wrong for Liverpool
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The passengers included a crew of eight, two infants, two Jamaicans nationals, an American, 82 Canadians, 35 Guyanese, a Pakistani and the Trinidadian.
"One of the wings came apart and the engine on the right side actually flipped over and we crashed into a big sand pile at the edge of a cliff".
Bedessee said takeoff had been delayed by about 45 minutes because one of the left-side doors had "not closed properly" and a maintenance crew was called to fix the problem.
"There were no reports of broken bones", Patterson told a news briefing at the airport.
Boeing said it was looking into the incident. A spokesman said consular assistance would be available to those who needed it.