Police in the British Overseas Territory were called to the property in the Boschetti’s Steps area at 11.35 this morning.
They found a 31-year-old man of British nationality, a 37-year-old woman of Spanish nationality, a four-year old girl of Spanish nationality and a baby girl who was six weeks old.
Detectives and forensic officers are working in the flat and the area remains cordoned off.
A spokesman for the Royal Gibraltar Police said: “It is believed that all the deceased belong to the same family.
“However, there are still inquiries being conducted to locate close relatives of the family and as you may understand it is for this reason that the identities of the deceased are not being disclosed.
“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 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.
“Her Majesty’s Coroner has already been informed and has visited the scene.”