The victim is 35-year-old Gladiz Polanco-Ramos, who lived nearby.
Police have ruled her death as a homicide.
Police say they received an anonymous call at about 1:30 on Thursday morning to go to the Dumpster in an alley along the 800 block of South Broad Street.
When officers arrived they found the nude body of Polanco-Ramos inside.
Law enforcement sources say a man has been taken in for questioning as a person of interest.
Detectives say they have been conducting numerous interviews and canvassing the neighborhood for any information that may assist in this investigation.
Police have not yet said how Polanco-Ramos died.