Police identified the suspect as Hunter M. Park from Rolla, Missouri, about 95 miles (150 km) south of the Columbia campus of the University of Missouri. He was not a student, they added.
Tensions are running high on the Columbia campus after the university's president and chancellor stepped down on Monday, following weeks of protests over their perceived weak handling of reports of racial abuse on campus.
The police said the suspect's threats had circulated on social media, including Yik Yak, where a posting tagged 'Columbia' on Tuesday read: "I'm going to stand my ground tomorrow and shoot every black person I see."
Yik Yak is an anonymous social media application that allows users to create and view posts within a five-mile radius.
Police said they arrested Park at about 1:50 a.m. local time (0650 GMT) under Missouri law which prohibits communication of a life-endangering threat to at least 10 people. He was transported to Columbia and is being held at the Boone County Jail on $4,500 bond.
On Twitter on Wednesday morning, the hashtag #PrayForMizzou was trending in the United States and postings highlighted the anonymous threat on Yik Yak. 'Mizzou' is the colloquial name for the University of Missouri.
Yik Yak spokeswoman Hilary McQuaide said the company had worked with police to identify Park saying the company may do so "when a post poses a risk of imminent harm."
Despite a heavier-than-normal police presence on campus, a few students decided to return home because they felt unsafe, students told Reuters.
University authorities said classes were operating on schedule. However, some professors, acting individually, canceled classes. Other teachers had given students the option of not attending classes if they felt unsafe.
On other U.S. campuses, peaceful marches or walkouts have been held this week, or are planned, over what some demonstrators see as soft handling of reports of racial abuse on campuses.
Soon after Missouri president Tim Wolfe announced he would step down on Monday, a crowd of more than 1,000 gathered peacefully at the Afro-American Cultural Center at Yale University in New Haven, Connecticut, for a "March of Resilience," in solidarity with Missouri.
The crowd sang and chanted for an end to racism on campus. The issue has been in focus at Yale after a fraternity turned away black guests at a Halloween party, saying, according to reports at the time, that only white women would be admitted.
A walkout is also planned at Ithaca College, a private school in upstate New York.
A student group called People of Color at Ithaca College announced on its Facebook page it was planning an on-campus 'Solidarity Walk Out' at 1:30 p.m. (1830 GMT) on Wednesday and demanded the resignation of Ithaca president Tom Rochon.
Students at Smith College, a women's private school in Massachusetts, plan a similar walkout for midday on Wednesday.