Chicago police said the 24-year-old woman was stabbed in the neck after having a "brief conversation" with a man inside the bank on the corner of Dearborn and Ohio in River North just after 11 a.m.
A man who did not want to be identified said he saw the suspect with a 5- to 6-inch knife.
"I saw a guy with a knife - a pretty big knife - with blood on it and he was running with a head of steam, and then, 30 seconds later, all the cops started coming then," he said.
The woman was rushed to Northwestern Memorial Hospital in critical condition, police said.
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On Thursday morning, officials said she was in serious condition.
A suspect was taken into custody Wednesday, and charges are pending in connection with the incident, Chicago police said.
A motive behind the attack is still unclear.
Area Three detectives are investigating.
Chase said it temporarily closed other branches in the area as a precaution on Wednesday.
On Thursday, the bank branch where the incident occurred was closed, along with a companion branch at Kinzie and Clark streets, Chase said.
The other branch is closed because it shares staff with the Dearborn location.
All other branches reopened as normal on Thursday.