Last month, protest group Animal Rising issued a call for volunteers to help disrupt the event by entering the track.
Surrey Police made 19 arrests in the build-up to the race, with a further 12 arrested at the racecourse "in connection with planned criminal activity".
"One man was arrested after he ran onto the racetrack after a race had started. He was quickly removed by event security and police officers, meaning the race was not disrupted," Surrey Police said in a statement.
Animal Rising shared a video of the protester being detained on Twitter, claiming that the individual was a supporter of the group.
"Our officers and event security responded quickly and decisively after a man ran onto the racetrack after a race had begun," Chief Superintendent Clive Davies said.
"We will not tolerate criminal behaviour which puts lives in danger, including those of the animals, jockeys, security staff and our officers."
April's Grand National was delayed by animal rights protesters, while more than 20 people were arrested at the Scottish Grand National.
Last year's Epsom Derby was delayed after six protesters from Animal Rising, then named Animal Rebellion, entered the course and had to be removed by the police.
