Mohammad Reza Ali Zamani was the first person to be sentenced to death in connection with the unrest triggered by President Mahmoud Ahmadinejad's disputed June 12 re-election, the human rights group said.
He was among about 100 people on trial since August accused of offenses ranging from rioting to spying and seeking to topple Iran's Islamic rulers through what authorities call a "soft overthrow."
Amnesty said it was concerned that the ruling against Zamani could open the way for more death sentences for those accused of similar crimes.
Zamani, 37, was convicted of "enmity against God" through membership in a group that seeks the end of the Islamic Republic and the establishment of a monarchy, according to Amnesty.
It also said he was also convicted of making propaganda against the ruling regime and of leaving the country illegally to meet with U.S. military officials in Iraq.
Several pro-reform Web sites have reported Thursday's ruling, but the government has not confirmed it.
Zamani testified in August that he met with a U.S. intelligence agent called "Frank" in Irbil, the capital of Iraq's self-governing Kurdish region, and received money and a phone from him in return for information on the Iranian government and student movements, according to state media reports at the time.
Rights groups and opposition figures in Iran have criticized the proceedings, calling them a "show trial" and saying such confessions are coerced.