Taskin had been suffering from an ankle injury but he recently started playing Dhaka Premier Division Cricket League.
The fast bowler, however, has failed to impress the selectors in the only match he played for Legends of Rupganj, reports UNB.
Imrul, on the other hand, has been superb throughout the last year for the Tigers. He played eight matches and scored 436 runs with two centuries. But he put up a dismal show in the ongoing Dhaka League.
He is in BCB's 20-member pool.
"The team management wanted a right and left-handed combination at the top order. So, we decided not to pick him," chief selector Minhazul Abedin said.
Left-handed batsman Soumya Sarkar got the selectors' nod. He played nine matches last year and scored 307 runs including a century against Zimbabwe. But his performance in the ongoing Dhaka League has also been poor.
"We're hopeful that he'll get back his form before the World Cup. He did well for the national team before," Minhazul said after announcing the team.
Taskin was dropped because of fitness. He was superb during the last season of Bangladesh Premier League. But he injured his ankle during the last match of Sylhet Sixers and had been sidelined for more than two months.
"He isn't fit enough. We considered him for the New Zealand tour after his good display in the BPL. But he was injured again," the chief selector said.
"He recently played a match in Dhaka League and it seems he's yet to be fully fit. But still, there's time. We'll consider him if any pacer gets injured in Ireland tour," Minhazul said.
BCB selectors called Abu Jayed Rahi in the ODI team for the first time instead of Taskin. The right-arm bowler is known for his ability to swing the ball. He took 11 wickets in five Tests and four wickets in three T20 Internationals for Tigers.
"Abu Jayed played Tests in New Zealand but did not get chance in the limited-overs cricket. We saw that he has the ability to swing the ball more than any of our bowlers. Since the World Cup is in England, we think he can be a good pick," Minhazul said.