Hasselbalch was born in Åstrup, near Hjørring, Denmark on 1 November 1874.
His parents were landowner and lawyer Hans Peter Jansen Hasselbalch (1843–1916) and Hedevig Alberta Rebekka Spärck (1845–76).
In 1879, his father remarried to Wilhelmine Marie Koppel (1858–1950=- Hasselbalch received his medical degree in 1898 and his doctorate in 1899 for his thesis on the respiratory metabolism in the chicken embryo.
[1][2] Hasselbalch was a pioneer in the use of pH measurement in medicine (with Christian Bohr, father of Niels Bohr), and he described how the affinity of blood for oxygen was dependent on the concentration of carbon dioxide.
Hasselbalch married Nanna Ida Elisabeth Heerfordt on July 26, 1904 in Hjørring.