Three other members of the same family are also in intensive care after the incident.
Two members of a family from Cardiff have died and three more are in intensive care in Bangladesh.
Bangladeshi Police said the family were staying in a flat near the north-eastern city of Sylhet.
Police officers broke into the building on Tuesday morning after relatives raised the alarm.
It is understood father Rofikul Islam and his son Michael, from Riverside, were found dead while his wife and two daughters were also taken to hospital.
The family was on a two-month visit to the country, local police said.
At first the incident was thought to be food poisoning but is now under police investigation.
Post mortem examinations have been carried out and further tests are due to take place.
This is a breaking news story and will be updated as we find out more.