Farshid Fathi was jailed in 2010 by intelligence officials after converting from Islam and openly preaching Christianity.
He was charged with "acting against national security through membership of a Christian organisation, collection of funds, propaganda against the Islamic Regime by helping spread Christianity in the country".
Pastor Farshid, 36, is married to Leila and has two children, Rosana and Bardia.
He was due to be released on 10 December and it is unclear why his freedom was held up.
The Christian was ordered to serve an extra year in prison in 2014 after prison staff claimed to have found alcohol in his cell.
He spent 100 days in solitary confinement when he was first jailed and has suffered a broken ankle at the hands of the brutal regime.
Elam Ministries, which works in Iran, said in a statement: "We are deeply grateful for your faithful prayers for Farshid while he has been in prison.
"We would like to request that you continue praying for Farshid today and in the coming weeks. Please pray especially for protection, his family and his adjustment to life outside prison."
Christian MP Stephen Timms called it "great news".
Listen to Premier's Antony Bushfield speaking to David Yeghnazar from Elam Ministries on the News Hour: