Detectives and forensic teams, including a coroner, are investigating the flat, which has been cordoned off.
A spokesman for the Royal Gibraltar Police force said that the deceased are believed to belong to the same family.
He added that officers are working to "establish the cause surrounding the untimely deaths of this young family and are encouraging anyone who maybe able to support the investigation to contact the duty officer of the Royal Gibraltar Police."
"Presently, we are not looking for anyone involved in this very unfortunate event, but the investigation will be thorough and detailed drawing in on the expertise of other professionals," he said.
The family's relatives are being sought before their names are publicly released, he added.
- Independent with additional reporting by PA