According to a post by the university on Twitter, officials say "a number of Black freshman students at Penn were added to a racist Group Me account". President-elect Trump is an alumna of the Ivy League institution's Wharton School of Business and his daughter Tiffany is a recent graduate.
Those incidents follow assorted reports of racial harassment at high schools in Pennsylvania which promoted Gov. Tom Wolf to react on Friday.
Some students posted on social media about the fear and sadness that they felt upon reading the texts. The messages, which appeared on mobile messaging app GroupMe, contained "violent, racist, and thoroughly repugnant images and messages", CBS News quotes the university as saying in a statement.
UPenn College Republicans responded with a post on their group Facebook page: "These messages are absolutely despicable". Every black member of the freshman class was apparently added to the group.
On Friday morning, several black students were added to a GroupMe thread called "Mud Men", according to the university's student newspaper, the Daily Pennsylvanian. And I have a lot of friends who are much more liberal than me.
The account sending the messages is believed to be based in Oklahoma, the university said, but campus police and security staff are still investigating the exact source of the messages. And we all stand together in solidarity with our Black students who have been so terribly targeted.
Campus protests popped up later Friday afternoon as students rallied to support each other.
"This is absolutely vile material and completely offensive to everyone on our campus", the statement read.
The university administrators said they have taken steps to increase campus safety in the wake of the racist messages. The people responsible for this are reprehensible. Another student, 22-year-old Brittany Brown, also said Trump's divisive language is "rippling through the country".
"Our university is extremely diverse, and ensuring that every last person feels welcome and safe is essential to our principles and our mission", NYU said in the statement.