Off-spinner Sunny and fast bowler Ahmed were reported by the umpires during a preliminary World T20 match against the Netherlands last week.
They were ordered to undergo tests in the Indian city of Chennai to determine if their actions breached rules designed to eradicate chucking.
Bangladesh bowling duo reported for suspect action
"Independent assessments have found the bowling actions of Bangladesh's Arafat Sunny and Taskin Ahmed to be illegal and, as such, both the bowlers have been suspended from bowling in international cricket with immediate effect," the ICC said in a statement.
The Bangladeshi team would be allowed to call up two replacements during the tournament subject to approval from the event's technical committee, the statement added.
Bangladesh face an uphill task to make the semi-finals of the World T20 for the first time after losing their opening match to Pakistan on Wednesday.
Asia Cup: Bangladesh stun Pakistan to reach final
Their next game is against Australia in Bangalore on Monday while they must also face New Zealand and India in the group stages.
The ICC launched a crackdown against suspect actions in 2014, which resulted in several leading bowlers being suspended, including the world's former number one-ranked spinner Pakistan's Saeed Ajmal.
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