The 27-year-old-man was arrested in La Chaux-de-Fonds at 1.30am following an investigation by the two forces, Vaud police said.
The dead body of a 29-year-old Swiss man of Kosovar origin was found on Monday with bullet wounds in a garage in Chavannes-près-Renens, west of Lausanne.
The discovery by a resident prompted a major probe by police, leading investigators to track down the suspect in an apartment where colleagues of his lived in the Neuchâtel city.
The arrested man, a resident of Lausanne, admitted to detectives that he had fired three gunshots in the direction of his brother-in-law, police said.
Officers seized a gun from the La Chaux-de-Fonds apartment.
Justice authorities have sought the provisional detention of the suspect.
According to the initial evidence the attack was linked to a family quarrel, Vaud police said.
However, the investigation is continuing to determine the exact circumstances of the homicide and to see whether others were involved, police said.
The police search for the presumed killer involved as many as 30 officers and a canine team with two dogs.