The 49-year-old man was based in the Trier police station in Rhineland Palatinate, and was authorised to carry a service weapon, which a police spokesman said was the one he used.
Police suspect that the man was upset about his wife's plans to file for divorce. The woman had told her husband on Thursday that she wanted to end the marriage.
Both husband and wife had adult children from previous marriages, but none of them lived at the family home in Saarlouis.
Police said the man apparently planned the murder-suicide meticulously, though it appeared he did not leave a suicide note.
"We believe that he was unable to cope with his wife wanting to divorce him," chief detective Dieter Erbel said.
An autopsy of the bodies is planned for Monday.