The 29-year-old's urine sample, provided in an in-competition test conducted on Nov. 13, was found to contain the presence of chlortalidone and he was subsequently provisionally suspended in December.
Chlortalidone is a diuretic drug which features in the World Anti-Doping Agency's (WADA) list of prohibited substances.
Shah pleaded guilty to the charge and said he had mistakenly taken his wife's blood pressure medication which contained the banned substance.
"While making the decision, the ICC accepted that Shah had inadvertently ingested the 'specified substance' for therapeutic reasons, specifically to treat his blood pressure," the ICC said in a statement.
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"He was able to satisfy the ICC through evidence and submissions prepared on his behalf by the Pakistan Cricket Board that he had no intention to enhance his sporting performance or to mask the use of another performance enhancing substance."
Shah's sample was taken in Abu Dhabi which hosted the second match of Pakistan's one-day series against England and the ban will rule him out of the World Twenty20 in India, starting from March 8.
A wily leg-spinner who has bagged 76 wickets in 12 tests, Shah has also played 15 one-dayers and can return to playing cricket again on March 27.
Shah said his case should be a reminder for all cricketers that they have to take responsibility and be extra cautious towards what goes into their body.
"I assure all fans and followers of the Pakistan cricket team that I have never taken a performance enhancing substance nor have I ever had the intent of masking any such substance," he said.
"I have always been careful to check my medication with doctors and medical support staff to ensure it does not contain any substance on the prohibited list.
"However, I acknowledge that I should have taken extra precautions to ensure that my blood pressure medication was stored separately from my wife's medication so that there was no possibility of my wife's medication being mistaken for my own."
(Reporting by Sudipto Ganguly in Mumbai; editing by Alan Baldwin)
