Skarsgård was born on 25 August 1976 in Stockholm, Sweden. He is the eldest son of actor Stellan Skarsgård and physician My Skarsgård. His parents are divorced. He has five younger siblings: Gustaf, Sam, Bill, Eija and Valter, and two half-brothers from his father's second wife, Megan Everett. Gustaf, Bill and Valter are also actors.

A friend of his father, a director, gave Skarsgård his first film role when he was seven years old, playing Kalle Nubb in Åke and His World (Åke och hans värld). In 1989, his lead role in the Swedish television production Hunden som log (The Dog That Smiled) earned him praise and brought him to prominence in Sweden at age 13. Uncomfortable with the fame, he quit acting at that same age.

At age 19, Skarsgård applied to perform his national service. He served in the Swedish Armed Forces, in the SäkJakt ("protect and hunt") unit that dealt with anti-sabotage and anti-terrorism in the Stockholm archipelago, for 18 months. After completing his service in 1996, he left Sweden and attended Leeds Metropolitan University in England for six months. He enrolled to study English but admits he did not study much and "had a blast" instead. While there, he considered pursuing an architecture career, but chose acting instead. In 1997, he enrolled in a theatre course at Marymount Manhattan College and moved to New York City. He returned to Stockholm after six months, but his time studying theatre confirmed to him that he wanted to act.
Was Alexander Skarsgård destined to become an actor?
Alexander Skarsgård was born into an actors family, his father Stellan as well as several of his brothers are successful actors. Furthermore, he got off to an early start when a friend of his father got him a role at seven years old, which seemed to suggest he was always destined to become an actor. However, along the way, several diversions could have set him on another path. At 13 years old he quit acting as he got uncomfortable with the fame. Later on, he joined the Swedish national service, went off to study English in Leeds, and considered pursuing an architecture career. But in the end, he chooses the path of acting.