CHICAGO—A Catholic high school cancelled classes Friday as tensions grew following a fatal police shooting that sparked competing protests and racially charged texts by students.

The unrest began with the Saturday shooting of a 25-year-old black man by a white off-duty Chicago police sergeant in the predominantly white neighborhood of Mount Greenwood on the city’s South Side. After protesters came to the neighborhood Sunday, a string of texts by several female Marist High School students upset with the demonstrators’ presence were shared widely on social media, adding to tensions in the enclave of mostly Irish- and Italian-American city workers.

On Saturday night, Joshua Beal was fatally shot by the police sergeant after an altercation with an off-duty Chicago firefighter. According to an initial statement from Chicago police, the sergeant came across the fight and saw that Mr. Beal had a gun in his hand. A screenshot from a private cellphone video of the incident authenticated by police shows that Mr. Beal was armed.

In its statement, the Chicago police said the sergeant stopped and exited his vehicle before displaying his weapon and announcing himself, but after Mr. Beal “failed to drop his weapon, shots were fired.” The sergeant is on administrative leave while the incident is investigated, police said.

Mr. Beal’s family, which couldn’t immediately be reached for comment, has disputed the police account.