Daphna Beerdsen, 31, who worked as a UN consultant in Cambodia, was found stabbed to death at her home on Monday.
Her daughter has been medically evacuated to Thailand for emergency treatment.
"We arrested the perpetrator last night, and we are working to gather more evidence," Phnom Penh deputy police chief Chuon Narin told AFP, declining to provide more details.
Another police official, who asked not to be named because he was not authorised to talk to the media, said the 32-year-old Cambodian man was arrested on Tuesday night at a Buddhist pagoda.
The suspect entered the victim's home in the early hours of Monday and tried to steal a bicycle, he said.
The man has confessed to killing Beerdsen with a screwdriver after she saw him trespassing and called for help, the official said.
The suspect also confessed to stabbing the baby, he added.
The victim had worked as a consultant for UN-Habitat, which promotes sustainable urban development.
The United Nations agency said in a message of condolence that it was "deeply shocked" at her death.