The British government said it had not received enough evidence to proceed with the case against Hadi Sulaimanpour, 47, whose arrest in August on an Argentine warrant damaged relations between London and Tehran.
"The warrant for provisional arrest has been cancelled because we did not receive enough evidence to proceed," a Home Office spokeswoman said.
But she said proceedings against the former Iranian ambassador to Argentina could be resumed if the South American country did come up with the necessary evidence.
Sulaimanpour, who has been free on bail pending a decision on whether to pursue the case, is wanted by Buenos Aires for his alleged role in the car bombing, which left 85 people dead.
Tehran strongly protested the arrest of Sulaimanpour, who has denied any connection with the blast.
"There is really no evidence at all implicating Sulaimanpour in the very serious crimes alleged," his lawyer Ben Brandon said.
Home Secretary David Blunkett in September received a 2600-page strong dossier from the Argentine government outlining its demands and proof against Sulaimanpour.
A court in October extended the deadline for a decision on the case by three weeks to November 13.
The British government has strongly pursued dialogue with Iran despite attempts by the United States to isolate the country which the US administration placed in an "axis of evil" along with Saddam Hussein's Iraq and North Korea.
"There is really no evidence at all implicating Sulaimanpour in the very serious crimes alleged"
Iran recalled its ambassador to Tehran for consultations after the arrest and demanded an apology from Britain, while Foreign Minister Kamal Kharazi warned of the devastating effects the case could have on relations between Britain and Iran.
Iran said the case was politically motivated.
Sulaimanpour was released in September on a $1.22-million bail, paid in large part by Iran, after a judge ruled there was little chance the father of two and doctoral student would try to flee the country.
He denies Argentina's accusations that he was involved in the July 1994 blast, saying he was outside the country at the time. The South American nation is home to the region's largest Jewish community.