"We are bringing in experts from across the country to clean up the oil," ExxonMobil Pipeline Company president Gary Pruessing said in a statement.
"We will stay with the cleanup until it is complete, and we sincerely apologize to the people of Montana for any inconvenience the incident is creating."
No cause has been identified for the release of oil from the pipeline, the company said, adding that it "met all regulatory requirements and has undergone inspection most recently in December."
ExxonMobil also promised "a thorough investigation" of the leak.
Considered one of the most scenic Western US rivers, the Yellowstone River starts in northwestern Wyoming and flows northward through Yellowstone National Park, feeding Yellowstone Lake and creating famous Yellowstone Falls.
It is one of the principal tributaries of the upper Missouri River.
Although the spill lies downstream from Yellowstone National Park, the river is seen as a major tourist attraction along all of its length.
The National Wildlife Federation said the spill highlights the dangers of such pipelines and is an argument for opposing a major pipeline to bring in oil from the Canadian tar sands.
"Oil and gas disasters are tragically common," the federation's Miles Grant said.
"Now the oil industry wants to build a new pipeline cutting right through America's heartland. The Keystone XL pipeline wouldn't carry just any oil -- it would carry tar sands, one of the dirtiest fuels on the planet."