Two shots were fired by Gurdeep Singh and the woman died on the spot even as her son fled the house to save himself.
Villagers later caught Gurdeep Singh and handed him over to the police.
The armyman was angry that his daughter married a man who was lower in social status and also belonged to the same village.
In some Punjab villages, marriages are not allowed within the village as boys and girls are considered brothers and sisters.
'We had sought police protection several times and had written to the police in this regard. But no action was taken. This unfortunate incident could have been avoided,' Balihar Singh said.
Local police officials said that the accused had been arrested and the matter was being investigated.