Durgaman Tamang, 33, and his wife Dil Maya Tamang, 28, were arrested in Lamjung district of western Nepal yesterday.
Another man involved in the crime is absconding, police said.
Police said they have confiscated weapons used in slaughtering the cow.
Police said the couple has been remanded to police custody for 10 days for investigation. A case has been filed at the district court against the..
Nepal became a secular state in 2008. Cow, which is sacred to the Hindus, was declared the national animal of Nepal in 2015 in the country's secular Constitution.
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