Sotoudeh told RFE/RL's Radio Farda that her passport was seized in an "absolutely illegal procedure" at the airport by agents who said they were from the "president's office."
Her husband and her young daughter were allowed to leave, but she and her son were not.
The prize, which is awarded by the organization Human Rights International, was to be awarded in the northern Italian town of Merano today.
Sotoudeh said in a letter to the organization that winning the prize will motivate her to increase her activities.
Sotoudeh was nominated for the award by Iranian Nobel Peace Prize winner Shirin Ebadi.