An employee was shot dead in a shop in Markdorf near Lake Constance on Saturday.
Her husband, who lives separately from her, was arrested as the alleged perpetrator.
The 47-year-old visited the three-year-old woman drunk in the general store around noon and shot her there, police and prosecutors said.
Other people were not injured.
After the fact, the man got into a taxi and fled.
The police were able to arrest him a little later.
The motive for the crime is still unclear.