Ibrahim Halawa was detained with three of his sisters when they were caught up in the Al-Fath mosque siege in Cairo.
The three women were allowed home to Dublin last November, but their 18-year-old brother remains in prison.
They had travelled to Egypt on holiday and said they sought sanctuary in the mosque when violent protests broke out.
The clashes took place between supporters of ousted president Mohammed Morsi and the security forces, who stormed the mosque and made many arrests.
Mr Halawa is now facing charges, along with hundreds of others in Egypt, over the protests.
The Halawa siblings are Irish citizens whose family moved to the Republic of Ireland a year before Ibrahim Halawa was born.
Their father, Sheikh Hussein Halawa, is the Republic of Ireland's most senior Muslim cleric.
The family lives in south County Dublin, where Mr Halawa is the imam at Ireland's biggest mosque in Clonskeagh.
The Irish government has provided diplomat support to the family since the four were arrested by the Egyptian authorities on 17 August 2013 and campaigned for their release.
However, exactly a year on, one of the three freed women called on the Irish and European authorities to do more to help her brother.
Somaia Halawa told the Irish broadcaster RTÃ‰ that Ibrahim went on hunger strike in the middle of last week, and has vowed to drink only water until his freedom has been secured.
She claimed the Irish government, and in particular, the European Union could end his hunger strike immediately by using their powers to guarantee his release.
Ms Halawa said: "Ibrahim will not stop this strike. This is his only, last resort."
An Irish teenager who has spent a year in jail in Egypt after he was arrested during a siege at a mosque has begun a hunger strike, his family has said.