The gunman, identified as Zephan Xaver, 21, called police after firing shots inside the SunTrust bank in Sebring, Florida, and eventually surrendered.
Karl Hoglund, Sebring police chief, said the shooting happened at about 12.30pm ET (17.30GMT).
Xaver called police to tell them he had fired shots, according to authorities.
Negotiators failed to convince him to leave the bank, at which point the Highlands County Sheriff’s Office SWAT team entered the building and continued to speak to him.
He surrendered and is in custody. His motive is not clear.
Mr Hoglund said: “Today has been a tragic day in our community.
“We’ve suffered significant loss at the hands of a senseless criminal doing a senseless crime.”
No information has been released about the victims.
CNN reported there had been no danger to the surrounding areas.
Ron DeSantis, Florida governor, said he was asking the state department of law enforcement to help local police.
Sue Malliano, a spokesman for the SunTrust bank, said: “We are working closely with officials and seeking to take care of everyone affected at our Sebring, Florida branch.”
