The man has been charged with aggravated assault, reports news agency Ritzau.
The dispute between the couple is reportedly a result of the man's jealousy, according to the report.
Duty officer Søren Strægaard of Southern Jutland Police confirmed to Ritzau that the man attacked the woman with the flat side of the axe.
Now under arrest and charged with aggravated assault, the man has been remanded in custody for 12 days and attended preliminary hearings at Esbjerg Court Sunday.
Den 45 årige mand fra Esbjerg blev i grundlovsforhøret fængslet til den 28. juli, for vold mod sin hustru. #politidk— Sydjyllands Politi (@SjylPoliti) July 16, 2017
The attack on the woman took place at around 2pm on Saturday afternoon and was reported to police by a family member.
No information is currently available as to the background of the incident other than that it was motivated by the jealousy on the part of the husband.
The woman was taken to hospital after the incident and is not reported to be in a life-threatening condition, despite the severe nature of the attack.