Amir Hekmati says Tehran is holding him hostage for use in a possible prisoner exchange, according to the letter addressed to Kerry and published by Britain's Guardian newspaper today.
Hekmati has been detained on what the US says are false espionage charges.
Family spokesman Greg Romano told The Associated Press today that Hekmati's sister, Sarah, authenticated the letter.
She says the handwriting is her brother's, as is the letter's tone.
The AP has sent an email seeking comment from the State Department.