Quinn said that all four pirates were on the lifeboat, after sinking their own boat after they seized the container vessel.
Earlier, the crew took one pirate hostage, trying to swap him for their captain, but the deal went wrong, he told the American CNN news channel.
No one appeared to have been hurt in the incident.
Maersk Line, the US subsidiary of Denmark's AP Moller-Maersk which owns the ship confirmed that the crew had regained control of the ship.
The Maersk hijacking comes just days after armed men took control of a British-owned ship, and the seizure of three other ships over the weekend.
There had been a relative lull in the number of hijackings in the first three months of 2009, with eight ships overrun by pirates in the Gulf of Aden, a main route for shipping travelling between the southern and northern hemispheres.
Somali pirates last year seized dozens of vessels close to the Somali coastline in their attempt to secure ransom payments, taking hundreds of sailors hostage.
The drop in the number of successful pirate attacks in the past three months is largely due to the increased presence of foreign navies in the area.
But the pirates have begun looking as far afield as the Seychelles in order to find unguarded ships to attack.
The gangs use speedboats launched from "mother ships" to give them an advantage over foreign navies patrolling the shipping lanes.
Pirates last year seized a Saudi supertanker containing $100m worth of crude oil.
The Sirius Star and its 25 crew were freed in January after $3m was dropped on to its deck.
Last September, a Ukrainian cargo ship carrying 33 Soviet-era T-72 tanks was also hijacked. It was released five months later after $3.2m was reportedly paid as a ransom.