A Sharjah resident rescued them on May 29 and took them to the aquariumwhere they are safe with more than 100 other local marine creatures.
Sharjah Museums Authority (SMA), which operates the aquarium, said the endangered turtles were handed to its staff a day after being rescued.
They are about 10 centimetres long and were initially kept in the nursery to make sure they were healthy.
Staff at the aquarium monitored their movement and swimming before moving them to display tanks.
Other turtles on display include the hawksbill turtle.
Green turtles live in shallow tropical and subtropical waters such as the Arabian Gulf and the Sea of Oman and feed on seaweed. The four will remain at the aquarium until they grow and can be released into their natural habitat.
Since 2011, the aquarium has released turtles into the sea three times — once in Al Khan, another in Kalaba and a third time in the Al Hamriyah area. Each group that was released included at least eight turtles.
The SMA's Director General Manal Ataya said it was the role of museums and aquariums to educate the public about the need to protect the environment.
“SMA has launched numerous initiatives such as the ‘Because We Care’ campaign to increase social awareness and preserve marine life,” she said.
The aquarium also launched a programme in 2011 to provide care and rehabilitation for sick and injured turtles before they are released back into their natural habitat, she said.
These programmes are run with the help of staff at public and private companies and members of the community.
Ms Ataya said the man who rescued the turtles this time had rescued two groups of injured green turtles in the past and handed them to the aquarium for treatment.
Green turtles are the largest hard-shell sea turtles, and their name refers not to the colour of their shell but the fat underneath it.