Alexander is the eldest son of actor Stellan Skarsgård and his first wife, a doctor named My.
He grew up in a Swedish working-class neighborhood with his five siblings: Gustaf Skarsgård (1980), Sam Skarsgård (1982), Bill Skarsgård (1990), Eija Skarsgård (1992) and Valter Skarsgård (1995).
In 2007 his parents separated and his father soon after rebuilt his life, expanding the clan in 2009 with the arrival of its sixth brother Ossian.