The 30-year-old, who has performed well domestically, was praised as a quality off-spinner by chief selector Salahuddin Ahmed on Sunday.
"Ajmal has impressed with his wicket-taking ability and can also bowl one which goes out like former spinner Saqlain Mushtaq and we hope he does well in this tournament," Ahmed told reporters.
Pakistan Thursday axed their specialist wicketkeeper batsman Kamran Akmal from a provisional squad of 20. Akmal's place went to newcomer Sarfraz Ahmed.
Pakistan take on Hong Kong in the opening Group B match of the six-nation Asia Cup here on Tuesday. India are the other team in the group.
Bangladesh meet United Arab Emirates in Lahore on Tuesday in Group A, which also includes defending champions Sri Lanka.
Squad: Shoaib Malik (capt), Salman Butt, Nasir Jamshed, Younus Khan, Mohammad Yousuf, Misbah-ul Haq, Shahid Afridi, Fawad Alam, Rao Iftikhar, Sarfraz Ahmed, Sohail Tanveer, Umar Gul, Wahab Riaz, Saeed Ajmal and Mansoor Amjad.