Kulasekara, 33, will be available for matches against Kent, Middlesex and Glamorgan. The club are expecting to have Mustafizur available for their last four T20 Blast group matches, as well as four Royal London one-day games, after his arrival was delayed following concerns over his workload.
Chris Jordan has also been made available for the match against Kent before returning to the England squad ahead of the final ODI against Sri Lanka in Cardiff.
Sussex are currently fourth in the South Group, three points behind leaders Glamorgan.
(Espncricinfo.com)