The problem in his left ear happened overnight around two years ago but Mr Robinson spoke about it publicly for the first time today.
His partner in government, Deputy First Minister Martin McGuinness, has suffered from tinnitus in his right ear for a decade.
Mr Robinson said: "I just woke up one morning to find I had lost the hearing of my left ear. My first reaction was to doubt that I could carry on my job.
"I did at first assume it would interfere too much with the discharge of my duties."
Around a sixth of the population in Northern Ireland, 300,000 people, suffer from hearing loss including tinnitus, which is characterised by a constant perception of noise in the ear.
The DUP leader said: "You work around it. After some weeks of saying nothing about my hearing impairment to colleagues I realised that nobody had noticed."
He added: "There are occasions when it is particularly difficult, if there is noise in the room that makes it difficult to pick up on what is said but life can be dealt with in a normal way by working around whatever disability you have.
"My officials know to approach me from the right side if they are going to whisper something during a meeting, waiters often get ignored if they come to the left side."
He joked about his relations with the deputy first minister.
"When I confided in Martin I discovered that he had a hearing deficit in his right ear so now you know the secret of how we work so well together.
"I can say whatever I like about him and direct it to his right ear and he smiles back and he can call me whatever he likes as long as he directs it to my left ear."
Mr Robinson told guests at the ceremony, it was important to learn how others had coped and added he was amazed at the number of people with hearing disabilities who held down pivotal jobs.
He added that the experience had taught him the value of understanding the huge difference between hearing and listening.
"One is a natural function, the other is a skill, the Executive is a listening administration committed to improving the lives of everyone in Northern Ireland," he said.
A draft physical and sensory disability strategy and action plan is under consideration by health minister Edwin Poots.
Mr Robinson told the audience: "In the leadership of the Executive you have two people who have some understanding of the issues that face your organisation and we will always be happy to encourage and support you in your work."
Mr McGuinness said: "I simply say thank you for everything that Action on Hearing Loss has done and continues to do.
"By empowering individuals you encourage them to recognise their potential by focusing on their abilities and moving their disabilities into the background.
"Hearing loss should not determine or limit opportunity."