It wasn't immediately clear if the shooting occurred inside or outside the building. Superintendent Johnson said the police arrested a suspect and found a gun.
In the incident, officers were on a routine patrol near the Tompson Center on Tuesday before seeing a person acting suspiciously.
Surrounding officers quickly arrived on scene and detained the suspect as well as his weapon, leaving bystanders in shock at the site they just witnessed.
Bauer was taken to Northwestern Memorial Hospital where he died and the suspect was taken into custody, said police Superintendent Eddie Johnson.
CTA said all buses and trains are running normal near and around the Thompson Center. Bauer was shot several times, Johnson said.
'I was walking down the street and I heard 'pop pop pop pop pop, " Noreen Danko, who was walking to her office nearby, told the Chicago Tribune. Within a minute, another officer said he saw the man.
"They just seemed to be searching him and taking off articles of clothing", Mr. Rodriguez said. "Maybe I'm jaded, I don't think that's anything to be proud of", he said.
During his tenure in the Near North District, Bauer spoke publicly about trying to rebuild trust in the community but also the frustration he felt about the "high bar to prosecution" when it came to career offenders.
"Our thoughts and prayers are with the family and colleagues of the officer tragically lost in a shooting at the Thompson Center today", Illinois Governor Bruce Rauner said on Twitter. He is survived by his wife and two daughters.