According to the newspaper, police involved in the shooting were answering an emergency-911 call reporting an attempted stabbing by a female suspect.
Columbus Mayor Andrew Ginther confirmed the fatal shooting, saying on Twitter that "a young woman tragically lost her life.
"The police officers involved had body worn cameras and the Ohio Bureau of Criminal Investigation (BCI) had opened an inquiry into the case, he said."We will share information that we can as soon as it becomes available," the mayor said on Twitter. "I'm asking residents to remain calm and allow BCI to gather the facts."
Family members have identified the girl killed in the shooting as Makiyah Bryant, aged 16.