Police said they have not made an arrest in the case and that the investigation remains open.
A police report says the young victim had been taken to Children’s National Hospital on Thursday afternoon for a “medical emergency.”
The report says the infant arrived unconscious and died at 2:44 p.m.
Police said the injuries occurred in the 1600 block of New York Avenue NE, between the neighborhoods of Ivy City and Brentwood.
The police report identifies the location as the Quality Inn and Suites. A spokeswoman for the D.C. Department of Human Services said the District contracts that hotel exclusively for homeless families.
According to the police report, the woman who took the infant to the hospital also has an address in Congress Heights in Southeast Washington. Attempts to reach the woman were not successful. Officials did not describe her relationship to the baby.