Butt said Afridi will play as an ordinary member of the team despite leading Pakistan to a 3-2 one-day series win over the West Indies earlier this month.
The switch is likely to be seen as punishment for Afridi's public criticism of coach Waqar Younis' alleged interference in team selection.
"Misbah will lead Pakistan in the two matches against Ireland and Afridi will play as a member (of the team) only," the Pakistan Cricket Board (PCB) chairman told a news conference.
Ireland host Pakistan for two matches on May 28 and 30.
The 31-year-old Afridi took over as Pakistan captain last year and guided the team to the World Cup semi-final where they lost to India – who went on to win the final – in March.
After the series against the West Indies, Afridi accused Waqar of meddling in team selection.
"Everyone should do his job and should be answerable for his duties," Afridi said. When asked about his differences with Waqar, Afridi replied: "They are not at a stage where we cannot resolve them."
The PCB asked Afridi to explain why he violated the code of conduct that prohibits players from speaking to the media on team affairs
Afridi replied by saying he did not name Waqar. On Monday, he left for the United States for a private family visit and he will join the team in Ireland.
The rest of the members were in the West Indies, where they play the second and final Test at St Kitts starting Friday.
Squad: Misbah-ul-Haq (capt), Younis Khan, Taufiq Umar, Mohammad Hafeez, Asad Shafiq, Azhar Ali, Shahid Afridi, Mohammad Salman, Saeed Ajmal, Abdur Rehman, Umar Akmal, Umar Gul, Wahab Riaz, Tanvir Ahmed, Junaid Khan and Hammad Azam