Workers received the call at the Red Cross's Jane B. Jennings Donor Center around 8:45 a.m., according to a Savannah-Chatham Metropolitan Police report.
"We received a call on an internal phone number indicating they were victims of Katrina and had not been treated fairly," said Dean Smith, the center's district manager.
The caller said "my family was a victim of Katrina and the Red Cross has done nothing for us. There is a bomb in the building and everyone is going to blow up and be dead," according to the report.
The Red Cross immediately called police and evacuated the building. About 20 people were inside, including staff, a training class and several donors, Smith said. The call forced the center to suspend operations for more than an hour.
Police found nothing suspicious.
The Red Cross in Savannah helped more than 800 Katrina-evacuee families, distributing more than $500,000, according to local Red Cross CEO Robin Wingate.