BCB cricket operations in-charge Shahriar Nafees confirmed to Cricbuzz that both players will not be available for the Zimbabwe T20Is as they are committed to franchise duties in Sri Lanka.
Litton is expected to return for the one-off Test against Zimbabwe, while Taskin could rejoin the ODI squad depending on selection.
Alongside Litton and Taskin, all-rounders Mehidy Hasan and Shakib Al Hasan, as well as pacer Hasan Mahmud, have also been granted NOCs for the LPL, which runs from July 17 to August 8.
Litton and Mehidy are set to represent Galle, while Taskin and Shakib will play for Jaffna.
The Zimbabwe tour begins with a one-off Test at Harare Sports Club from June 28, followed by three ODIs on July 6, 9 and 11, all at the same venue. The series will conclude with three T20Is in Bulawayo on July 15, 17 and 19.
BCB officials also noted that the Test squad will travel in phases, with the first group departing Dhaka on June 21. Some players will join later depending on their white-ball commitments and fitness management.