Bari said Pakistan Cricket Board (PCB) had advised the selection committee against picking the bowler for the July 16-August 2 tournament, also involving archrivals India, to be held in Sri Lanka.
"PCB chief executive Rameez Raja has informed us in writing not to consider Shoaib Akhtar for selection for the Asia Cup," Bari said in Karachi.
Bari cited "fitness problems" as the reason for the bowler to miss out on the important series.
"These things happen in international cricket. Even Australia rested their pace spearhead Glenn McGrath for quite a few months because he was not fit," he said.
The former player also said Shoaib was likely to pull out midway from his stint with English County team Durham owing to fitness problems.
Raja said that PCB was only acting on the advice of Durham and was resting the bowler keeping in mind the ICC Champions Trophy in September.
"We received suggestions from Durham that we should use Shoaib sparingly. We have had discussions among ourselves and have written to the selection committee about Durham's advice," Raja said.