The two - a 41-year-old man and 26-year-old woman - were among five members of the same family who became sick after returning from a trip to the town of Marivan, close to their home in the northwestern city of Kermanshah.
The three surviving relatives were still in hospital and one of them remained dangerously ill, the official who spoke on condition of anonymity said on Monday.
It was not clear when the brother and sister died.
Samples have been sent to international laboratories for further tests, and if the initial results are confirmed, these would be the first human bird flu deaths in Iran.
Confirmation of H5N1 could deal a major blow to Iran's poultry industry.
The Union of of Chicken Meat Farmers says the industry employs 600,000 people directly but as many as 3 million people are dependent on it.
Third person in coma
A third family member, aged 30, had slipped into a coma in hospital in Kermanshah, which is 100km from the Iraqi border in the mountainous Kurdish territories of Iran.
Iran first detected cases of bird flu in February, when the virus was found in wild swans.
All Iranian officials contacted said they had been instructed not to speak to the media, adding that only the health minister was authorised to comment.
The H5N1 virus remains mainly a virus of birds, but experts fear it could change into a form easily transmitted from person to person and sweep the world, killing millions within weeks or months.
The virus has killed 123 people since late 2003, most of them in Asia, according to the most recent figures from the World Health Organisation.
Iran's neighbours Turkey, Iraq and Azerbaijan have all reported deaths from the virus in recent months.
So far, most human cases can be traced to direct or indirect contact with infected birds.