Jaish al-Adl is a little known organisation that operates in Iran's border area with the neighbouring country.
Semiofficial Fars news agency said in a report on Monday that the five Iranian guards have reportedly been taken to Pakistan.
Jaish al-Adl's name was raised for the first time in October when they killed 14 Iranian border guards in an ambush.
Iranian authorities hanged 16 members of the rebel group in retaliation for the ambush.
Jaish al-Adl is widely believed to be a Saudi-backed ultraconservative salafi group which aims to punish the Islamic Republic for its support of Syrian President Bashar al-Assad.