The official IRNA news agency, in a report on the court's move late on Wednesday, did not mention Rafsanjani, who backed opposition leader Mirhossein Mousavi in last year's disputed presidential election.
IRNA said a Revolutionary Court in Tehran decided to ban the Hemmat weekly due to "slander and dissemination of lies with the intention of agitating public opinion."
The Rahesabz opposition website said it was a conservative publication which had been banned also a year ago for insulting Rafsanjani, who remains influential in the Islamic Republic.
There was no official comment on the Rahesabz report.
The latest issue of Hemmat — the sixth since the previous ban was lifted — carried a front-page picture of Rafsanjani, surrounded by known critics and opponents of the Islamic state, with the headline "All the disciples of Hashemi."
Earlier this week, the semi-official Fars News Agency said Hemmat had received a warning for carrying the picture.
"Putting the pictures of some respected officials next to some other individuals is inappropriate and a non-professional act and would imply raising accusations against the officials," Fars said, citing an official statement.
Last June's vote, which the pro-reform opposition says was rigged to secure hardline President Mahmoud Ahmadinejad's re-election, plunged Iran into turmoil and exposed deepening establishment divisions. Authorities deny opposition charges that vote was rigged.
(Writing by Fredrik Dahl; editing by Samia Nakhoul)
