The Maritime and Port Authority of Singapore (MPA) said the vessel, part of the giant Maersk Line fleet, was en route to the group's terminals in the south Malaysian port of Tanjong Pelepas.
No reports of injury or oil pollution have been received by the MPA and the authority, which has launched an investigation into the incident, said shipping in the area and in adjacent waters had not been affected by the grounding.
"The vessel is in stable condition and the shipowners have arranged for a salvage company to attend to the grounded vessel," the MPA said in a statement.
The 6,500 TEU Maersk Kendal was built in 2007 by the Hanjin shipbuilder in South Korea and delivered in 2008.