Fighter jets attacked what was said to be “a large gathering of Boko Haram terrorists” at the Durwawa settlement, near Urga in the Konduga area of Borno state on October 19.
The bombing killed jihadists on the ground and triggered a fire, air force spokesman Air Commodore Olatokunbo Adesanya said in an emailed statement.
“Efforts are ongoing to confirm the reported killing of Shekau’s wife, alongside other BHTs (Boko Haram terrorists),” he added.
The woman was identified only as Mallama Fitdasi. Mallama is an honorific in Hausa that translates as “madam”.
Adesanya said Fitdasi was “reported to have been representing her husband in a coordinating meeting with other terrorists at the location of the airstrikes”.
Shekau, a shadowy leader known for his lengthy, wild-eyed video messages, took over as leader of the group in 2009 after the death in custody of its founder, Muhammad Yusuf.
Shekau was known to have four wives, including one of Yusuf’s widows.
Another wife, Hassana Yakubu, was arrested in an army raid in the northeastern city of Damaturu in 2012.
She was released the following year with another of Yusuf’s widows, Mallama Zara, plus the wives of several other top commanders.
Boko Haram, whose eight-year Islamist insurgency has left at least 20,000 dead in northeast Nigeria, has long been factionalised.
But last year it suffered a major split, when the so-called Islamic State group recognised Yusuf’s son, Abu Mus’ab al-Barnawi, as leader.
The United States has designed Shekau as a global terrorist and offered a reward of up to $7 million for information that brings him to justice.
In August, Nigerian forces conducted an unauthorised dawn raid on a UN compound in the Borno state capital, Maiduguri, after rumours on social media that Shekau was hiding there.
Nigeria’s security forces have previously declared Shekau to be dead on at least three occasions, only for him to resurface in taunting video messages.