The Danish-flagged vessel, Mumbai Maersk, is situated about 6km north of the East Frisian Island of Wangerooge, where it got stuck at 11.05pm on Wednesday as it headed from Rotterdam to Bremerhaven, the German Central Command for Maritime Emergencies said.
The operation to free the ship began overnight, with several tugboats and multipurpose vessels dispatched to the scene.
A team of specially trained seafarers was also brought on board.
A first attempt to bring the container ship back into deeper water failed, a spokesperson for the command said.
A high tide later on Thursday also proved insufficient to get the ship moving.
Maritime salvage experts are now waiting for the next high tide, at around 2am on Friday, to get the vessel into deeper water.
"Fortunately, there are no injured persons. Everyone is well," the German command spokesperson said.
The ship, which originates from Asia, was only partially loaded when it ran aground on its way to the Bremerhaven port.
"All crew are safe, there is no pollution and no sign of hull breach," Danish logistics company Maersk wrote on Twitter.
The cause of the incident was not immediately clear.
Online shipping trackers show that the Mumbai Maersk sailed in a tight circle before bumping up against the bottom of the Wadden Sea.
The local water police have launched an investigation, a spokesperson in the German city of Oldenburg said.
There was a similar incident at the weekend off the East Frisian coast, when an unloaded freighter got into trouble during a powerful storm.
In the end, it was able to continue its journey to Denmark without additional assistance.
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