Batsman Mushfiqur Rahimall-rounder Mehidy Hasan Miraz and pace trio Taskin Ahmed, Hasan Mahmud and Shoriful Islam were all rested alongside Shakib.
Naim Sheikh, Afif Hossain and Shamim Hossain, who also played in the Asia Cup, have been ruled out, the Bangladesh Cricket Board said in a statement.
Opening batsman Litton Das will lead the team which marks the return of senior batsmen Tamim Iqbal and Mahmudullah Riyad along with Soumya Sarkar and Nurul Hasan Sohan.
Tamim has not played a match since his retirement against Afghanistan in July, while Mahmudullah played the last of his 218 ODIs against England in March.
Uncapped opener Zakir Hasan, paceman Syed Khaled Ahmed and leg-spinner Rishad Hossain have also made it into the squad.
“The decision to rest the players was taken with consideration World Cup in India, which will be a long tournament where it will be very important to ensure the mental and physical fitness of the cricketers,” said chief selector Minhajul Abedin.
“The series against New Zealand gives us an opportunity to look at some other players ahead of this big event,” he added.
Minhajul said newly-signed Zakir was very close to playing against Ireland in March before suffering an unfortunate injury.
“Khaled has done well in his List A career and Rishad offers another dimension to our bowling attack,” he said.
New Zealand will arrive in Dhaka on Sunday for the series starting on September 21 at the Sher-e-Bangla National Stadium in Dhaka.
The second and third ODIs will be held at the same venue on September 23 and 26.
The series will be the last for both teams before the start of the World Cup in India on October 5.
Bangladesh, who failed to qualify for the finals in the ongoing Asia Cup, won their previous two home ODI series against New Zealand 4-0 in 2010 and 3-0 in 2013.
New Zealand will also play two Tests in Bangladesh after the World Cup ends on November 19.
Bangladesh Team: Litton Das (captain), Tamim Iqbal, Soumya Sarkar, Anamul Haque, Tawhid Hridoy, Mahmudullah Riyad, Nurul Hasan Sohan, Mahedi Hasan, Nasum Ahmed, Mustafizur Rahman, Tanzim Hasan Sakib, Tanzid Hasan Tamim, Zakir A Hasan, Khasled
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