Face of Nation : Mr Frazer is currently receiving treatment in Craigavon Area Hospital and is understood to be critically ill.
A complaint over the sharing of the image on social media was made to the Trust by Ulster Unionist MLA Doug Beattie.
Mr Beattie said the image was “a terrible invasion of his privacy”.
In a statement the Trust said: “We are looking into this matter.
“To protect the confidentiality and dignity of our patients, we have a policy which states that any photograph of a patient is not allowed to be taken without the prior permission of the Trust.”
Speaking to BBC Radio Ulster’s Evening Extra, Mr Beattie said he saw the picture on Twitter.
“It was very clear that this picture had been taken without his permission,” he said.
Mr Beattie said the Trust had replied immediately to his complaint and confirmed it would be looking into it.
Willie Frazer was the founder of Families Acting for Innocent Relatives (Fair), a group set up in 1998 to support victims of republican violence.
His father Bertie, a part-time member of the Ulster Defence Regiment, was killed in an IRA gun attack in 1975.
