Ka Yang, 29, was taken into custody at her home in Sacramento, capital of California, The Los Angeles Times reported.
Officials said they were trying to understand what they described as a horrific crime.
"We don't know what motivated her to do the crime. We don't really know what led up to it," sergeant Norm Leong of the Sacramento Police Department was quoted as saying.
The mother has been charged with homicide, the report said.
Investigators have concluded that the baby's burns were not explainable, Leong said. He said detectives sought out forensic experts for advice.
"This was definitely unique. Detectives realised they would have to look beyond what they normally do... and found experts who said the injuries appeared to be from a microwave," he said.
