Joel Cox was arrested on May 5 from Jinnah International Airport here for carrying 15 bullets and three small knives before boarding a plane for Islamabad.
Police today presented final chargesheet in a district court in Karachi.
Judge Hasan Ali Kalwar after hearing arguments of Cox's lawyer rejected the allegation, which he said were based on a misunderstanding.
He also said that the accused was not carrying any weapons at the time of arrest and the anti-terror laws invoked by police do not apply in the case.
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While discharging the accused, the judge also ordered that Cox's belongings should be returned.
The quiet dismissal of the case is in sharp contrast to the furor after arrest of CIA contractor Raymond Davis who killed two men in Lahore in 2011.
Right wing parties had protested against Raymond's release after paying an unspecified amount of blood money to the heirs of victims.