The fire broke out late Tuesday evening in a residential building in the center of the small town of Miranda de Ebro.
Surveillance footage shows a man throwing lighter fluid into the building's entrance and calmly walking away.
The three victims were aged 23, 58, and 78. Four more people, including two children, were injured.
A former partner of one of the victims was wanted by police early on. The man went to the police himself and is now in custody, Spanish media report.
According to police representatives and the Spanish government's special delegation against gender-based violence, the investigation is treating this as an unusually extensive case of gender-based violence.
