Velásquez was born in February 1947 in Pharr, Texas. He was the third of nine children born to Cresencio and Vicenta Castillo Velásquez. Baldemar's father was born into a Mexican American family in Driscoll, Texas. His grandfather died when Cresencio was just 11 years old, forcing the young Cresencio to seek employment as a migrant worker. Baldemar's maternal grandparents fled to Pharr in 1910 after the Mexican Revolution, and his mother, Vicenta, was born there in 1920. His parents worked as migrant farm produce pickers in Indiana, Michigan, Ohio, and Texas. Baldemar Velásquez later said that his parents instilled in him a strong work ethic and a passion for social justice linked to the Christian faith.