Monaghan was born in Berlin, Germany. At the age of twelve, his family moved from Germany to Heaton Moor in Stockport, Greater Manchester, and later to Manchester. Monaghan's first language is English, but he also speaks German and is well known for his ability to impersonate others and replicate accents. He attended St. Anne's RC High School (where his uncle taught and later became head teacher) and Aquinas College, where he studied English literature, drama and geography.

Although he had many occupations when he was younger, he always wanted to be an actor. After his second year at Aquinas, he became a regular in school plays such as Oliver Twist, A Christmas Carol, and Bugsy Malone. Monaghan then went on to join Manchester Youth Theatre where he was scouted for Hetty Wainthropp Investigates. He played Hetty's under-aged sidekick, Geoffrey Shawcross, for four seasons. He made his feature film debut as Russian sailor Sasha in TV film Hostile Waters.