Yemeni authorities said they had stepped up security following the announcement.
Analysts say Yemen is of huge significance to al-Qaeda.
"Weapons, training, crossing points and the launch of operations have all come from Yemen," Abd Alelah-Haidar, a "terrorism" specialist who has met Wuhaishi, told Al Jazeera.
"This country is seen as having strategic significance, not only by al-Qaeda, but also by others. [However,] their operations are not confined to the Arabian peninsula but also include Iraq, Afghanistan, Nahr al-Bared [in Lebanon], and Palestine."
The announcement follows a number of attacks by al-Qaeda in Yemen.
An attack outside the US embassy in Sanaa earlier in the week is believed to have been carried out by the group.
Yemeni police arrested three men on Monday after they fired on security forces near the embassy. No one was hurt in the incident.
Nineteen people died in an attack targeting the US embassy last September for which al-Qaeda claimed responsibility.