Tanaya Lewis, 17, is accused of murdering Danya Gibson, 16, after the pair got into a fight over a boy.
Lewis allegedly used a kitchen-style steak knife to stab her classmate twice in the chest at around 8.30am on Wednesday.
Danya was taken to hospital but died later that day, according to Click On Detroit.
Tanaya was arraigned on Friday and charged with first-degree murder. She could face life in prison without parole.
During her arraignment on Friday in Michigan, USA, a prosecutor said: “Witnesses said the defendant was smiling and laughing as she was chasing the victim.”
She was not granted bail.
In a statement, the school, which cancelled all lessons for the rest of Wednesday and Thursday, said it was “deeply saddened” by what happened.
It said: “Our hearts and prayers go out to the student’s family and we offer our deepest sympathy.
“Students at Fitzgerald High School were released at 10am. On Thursday, September 13, Fitzgerald High School will be closed however the middle school and elementary schools will be open.
“At the high school we have deployed additional counselors, psychologists and social workers for students and staff who need support during this difficult time.
“Students and their parents may come to the High School between the hours of 8am and 2pm. for support and assistance.
“We are working very closely with the police department on this matter as well as conducting an internal school review of the incident which will review all our current safety procedures and protocols.
“This is a time of mourning for the Fitzgerald Community and we ask for you to respect the privacy of the victim’s family.”