In a letter addressed to the council, Ebadi, who is a lawyer, calls for Esfandiari's release and for a "fair and open trial."
Ebadi told Radio Farda she decided to write to the UN body because Iranian judiciary officials ignore her legal demands including access to Esfandiari, who is her client.
"I have always repeated that we hope all our problems can be solved by judicial officials in Iran, but since I see that, inside Iran, no attention is paid to my legal demands as a lawyer, I have to use all legal possibilities that are available domestically and internationally to help my client," said Ebadi.
She said Esfandiari has been kept in solitary confinement for three months on suspicion of harming national security.
Several human rights groups and the United States have called on Iran to release Esfandiari and two other Iranian-Americans who are currently jailed in Iran.
Kian Tajbakhsh, a consultant with the Open Society Institute, and peace activist Ali Shakeri are reportedly also facing security charges.
Rights groups have also called on Iran to allow Radio Farda broadcaster Parnaz Azima to leave the country.
Azima’s passport was taken from her upon her arrival in Tehran in January.
(with material from agency reports)