17-year-old Md Israfil and 15-year-old Robeya Khatun were married about eight months ago
A speedy trial tribunal in Dhaka announced the verdict on Wednesday.
According to the case document, Rafiqul Islam murdered his wife Rehana Akter Bokul on May 6, 1997 at Jatia village of Mymensingh's Bhaluka Upazila.
He used to work as a police constable at Dhaka's Rajarbagh Police Lines at that time.
While on a visit to his hometown, Rafiq strangled Rehana during an argument over land.
He later claimed that Rehana had committed suicide.
Rehana's mother Sobura Khatun filed the case at Bhaluka Police Station accusing Rafiq, his brother, sister and uncle for the murder.
Police pressed charges against all of them, but the court on Wednesday acquitted the other suspects.