Tweets from known AQAP operatives also spoke of al-Wuhayshi having been martyred, and of AQAP military commander Qasm al-Rimi (also known as Abu Hureira al-Sanaani) having been appointed as al-Wuhayshi's replacement.
U.S. authorities are looking to confirm al-Wuhayshi's death, according to one U.S. intelligence official.
Al-Wuhayshi was the No. 2 leader of al Qaeda globally and the head of AQAP. In a video that surfaced in April last year, the man who was known as al Qaeda's crown prince appeared brazenly out in the open, greeting followers.
In a speech to the group, al-Wuhayshi makes it clear that he's going after the United States, saying: "We must eliminate the cross. ... The bearer of the cross is America!"
The video showed what looked like the largest and most dangerous gathering of al Qaeda in years.
Originally from Yemen, al-Wuhayshi assumed command of AQAP in 2009. He'd escaped a Yemeni prison in 2006, and had previously worked as a personal secretary for Osama bin Laden.
"If it's true, it is a significant blow. Leadership matters," Sen. Angus King, an independent of Maine, told CNN on Monday.
King said the death would hurt al Qaeda, but stressed the group still poses a threat.
"This is a long, difficult struggle that we're engaged in, and it's going to require all kinds of tools," King said.
Reports of al-Wuhayshi's death come shortly after U.S. planes carried out a strike inside Libya, purportedly killing a key terror figure in North Africa.
The target was Mokhtar Belmokhtar, a veteran Islamist fighter, who is blind in one eye, affiliated with al Qaeda in North Africa, a U.S. official told CNN.
The Libyan government said Belmokhtar was killed in the weekend strike, something that U.S. officials have not confirmed.