Facebook, which claims to have 175 million users worldwide, expressed its disappointment over the reported ban. So far there has been no comment from the authorities in Tehran.
Mousavi was Iran's prime minister when the post was abolished in 1989
It said that "according to certain Internet surfers, the site was banned because supporters of Mir Hossein Mousavi were using Facebook to better disseminate the candidate's positions".
CNN staff in Tehran reported that people attempting to visit the site received a message in Farsi that said: "Access to this site is not possible."
Facebook expressed disappointment that its site was apparently blocked in Iran "at a time when voters are turning to the Internet as a source of information about election candidates and their positions".
Mousavi is seen as one of the leading challengers to incumbent President Mahmoud Ahmadinejad in the 12 June elections.
His page on Facebook has more than 5,000 supporters.