The incident took place at the Upazila's Hartukitala village around 8:30 pm on Saturday, said Kaliakair Police OC Alamgir Hossain Mazumder.
The dead are Fahima Akther, 30, and her ex-husband Miktula Miah, 35,.
The couple had separated five months ago after two-and-a-half years of marriage.
The victim, Fahima, was living in Hartukitala village with a female friend. She used to work in a garment factory in the Kaliakair Municipality area.
Miktula went to Fahima’s house at night and began to stab her with a knife. He tried to escape as neighbours rushed to the scene after hearing her screams, police said citing local residents.
Both of them were rushed to Upazila Health Complex, where doctors declared them dead, OC Mazumder said.
There was no relationship between the two after their separation five months ago, Intaz Ali, Fahima's father told bdnews24.com.
'My daughter used to live with one of her female friends and worked in a garment factory. We don't know why she was killed," he added.