Injured proprietor Paramjit Singh's daughter said the two people have been customers at the shop, who had had credit for such items as milk and bread when times were tough.
It was a dispute over a squashed loaf of bread which apparently sparked Wednesday's incident, which happened as two boys apparently with the man waited outside.
The man was seen to squash a loaf of bread, and CCTV images show him fleeing moments later as members of the family took to him with a stick.
A customer rang police who were understood to have been on their way when the woman arrived with an axe.
She was said to have discarded the axe as she fled, and while she was soon apprehended the man was yet to be located, Ms Patrick said.
"We know who he is," she said. "We have made inquiries so he knows we are looking for him. We'd like him to take the opportunity of giving himself up."
The Singhs have lived in Hastings "for years" and bought the shop from friends about seven months ago, Mr Singh's daughter said.
She said customers in the area had been good to the family, and some called and visited yesterday, offering apologies on behalf of their community and best wishes for Mr Singh, who was sporting two severely blackened eyes.
The arrested woman will appear in Hastings District Court on January 9.
