The actor, who plays David Platt in the ITV1 soap, issued a statement after a woman told the News of the World he had a one-night stand with her last month.
Platt, 22, who has a baby daughter called Nyla with his long-term partner Lauren Shippey, said he was "deeply sorry" for letting down his family and employers.
He said: "On Sunday, there were some articles printed about errors I have made in my private life.
"Over the years, I have enjoyed a successful career with Coronation Street, and with this I have experienced privileges that have exceeded my own expectations.
"The core ingredients to my success have come from the following areas; my family, ITV Granada, and specifically my girlfriend Lauren and daughter Nyla.
"I would like to apologise to my family, for all the hurt and pain I have caused them, to ITV Granada for letting them down, and especially to Lauren and Nyla, who are the most important people in my life.
"I now need to concentrate on what is really important, my family and my career, as I have abused my position as an employee, partner and father, and for that I am deeply sorry."