Monday's statement by the Kuwait Oil Co. did not identify the onshore oil field affected by the leak, which began Sunday.
The state-run Kuwait News Agency said the leak hit the al-Maqwa field.
The company said there's no sign of a toxic gas leak. It offered no details about how many barrels of oil had been spilled.
OPEC member Kuwait is a major oil producer. The U.S. Energy Information Administration says Kuwait produces some 2.7 million barrels of crude oil a day and holds the world's sixth-largest oil reserves.
In August, Kuwait announced a spill at its Ahmadi field. A February fire struck another oil well after a spill.