Video footage posted to social media also showed demonstrators climbing on the bronze monument in Lafayette Square, across the street from the White House, in the latest bid to destroy images of historical figures considered racist or divisive.
Police in riot gear are then seen moving in to drive the crowd back and form a protective ring around the statue, which was erected in 1852 on a white marble base and depicts Jackson astride a rearing horse.
Earlier, protesters clashed with police in the nearby streets, the latest in a string of demonstrations against police brutality and racism following the death of a 46-year-old Black man, George Floyd, under the knee of a Minneapolis police officer.
Jackson, the seventh U.S. president, was a former general in the U.S. Army and a populist politician nicknamed "Old Hickory," whose political style has sometimes been compared with that of President Donald Trump.
Native American activists have long criticized Jackson, a Democrat, for signing during his 1829-37 presidency the Indian Removal Act, in which thousands of people were driven from their land by the U.S. government.
Forced to march West in what was described as the "Trail of Tears," thousands of Native Americans died before reaching their intended destination.