Police would not comment on the cause of death, saying only that the probe was being treated as a murder investigation but they were not looking for anyone else.
"At this present moment in time, a full investigation is being conducted by officers of the Serious Crime Unit to establish the cause surrounding the untimely deaths of this young family," Royal Gibraltar Police chief Eddie Yome told a news conference.
The dead include a 31-year-old British male and a 37-year-old Spanish woman.
The authorities said they believe the four belonged to the same family which had recently moved to the tiny British territory.
Gibraltar Chief Minister Fabiano Picardo adjourned parliament until Wednesday after receiving news of the deaths.
"As a husband and father, I -- like no doubt all Gibraltarians and residents of Gibraltar -- am in total shock to hear about this terrible crime," he said in a statement.