Layla Abd Allah Saad, dean of the college of law at Mosul university, and her husband, Munir al-Khiru, were found dead at their house early on Tuesday.
Police officers on the scene said preliminary indications showed Saad had been shot dead, while her husband had his throat slit. There were no signs to suggest a robbery had taken place, they said.
"Layla and her husband were our neighbours," said Fakhri al-Numa, who lives near the house in a neighbourhood of southern Mosul.
"We tried to contact them, but nobody has been answering the phone since yesterday. We went into the house and we saw they had been killed."
According to relatives, Saad used to teach law in Bahrain until returning to Iraq after Saddam Hussein was ousted in April 2003. Four months ago, she was appointed dean of the Mosul law school.
Her husband was a retired accountant and family members said the pair had no connection with the former Baath regime.
A wave of academics, including former Saddam associates, have been killed in the Sunni Muslim city, 370km north of Baghdad, since the US-led invasion of Iraq in March 2003.
Police offered no immediate explanation of the motive.