Iran said questions from the host of the "Without Borders" programme had questioned the legitimacy of Sistani's leadership in Iraq.
Hadad Adel said: "This is a plot of the enemies of Islam and Iraq and news networks like Al Jazeera committed this insult because of their influential role."
Earlier ban
The Iranian-born al-Sistani is Shia Islam's leading cleric and commands huge respect in both Iran and Iraq.
Last week he held talks with Ali Larijani, Iran's top national security official, in the Shia holy city of Najaf.
The new furore about comments made about the cleric recalls a similar controversy in December 2005 when Iraqi Shias protested against the channel after a talk show guest accused Sistani of favouring the US occupation.
After that incident, Tehran summoned the ambassador of Qatar, where Al Jazeera is based.
Al-Jazeera's Tehran bureau was shut down by the authorities in April 2005 amid accusations of stirring up violence in its coverage of clashes in the ethnic Arab majority city of Ahvaz and only reopened 14 months later.