The service member was identified as Christopher Paul Conway, 22, stationed at Fort Campbell, along the Kentucky-Tennessee border.
"We discovered the child had been sexually assaulted, and a cord had been placed around the child's neck and the child died from those injuries," Clarksville, Tenn., police department spokesman Jim Knoll told Nashville's Fox 17.
Police responded to a 911 call Tuesday morning to find someone performing CPR on the infant, before she was taken to a nearby hospital and pronounced dead, Nashville's WKRN-TV reported.
An investigation led to the arrest of Conway, who later admitted to the crime, WKRN reported.
Army officials confirmed to Fox 17 that Conway was a U.S. combat medic specialist at Fort Campbell.
Conway was booked Wednesday in the Montgomery County, Tenn., jail and was being held on a $100,000 bond, WKRN reported.