Pakistan Test captain Misbah-ul-Haq was also tested by the International Cricket Council (ICC).
The team can ill afford any positive results, which could have a significant impact on their upcoming tour in England, during which the results are expected to be confirmed.
The ICC, which has been a signatory of the World Anti-Doping Agency (WADA) since 2006, routinely conducts such tests in and out of competition.
Shah was provisionally suspended in December last year after he tested positive for chlortalidone, a masking agent under the WADA list of banned substances.
His ban was lifted in late March, making him eligible for the England tour.
Alam said Shah's test could come under the spotlight.
"Besides Shah, Test captain Misbah-ul-Haq, one-day skipper Azhar Ali and fast bowler Junaid Khan were also tested but Shah's test could be targeted," he told AFP.
Shah is seen as Pakistan's main wicket-taker for the four-match Test series in England, which starts at Lord's from July 14.
Pakistan will also play five one-days and a Twenty20 international on the tour.
Amir returned to the national team in January this year and is expected to be named for all three formats for the tour.
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