Fabius said that his Iranian counterpart Mohammad Javad Zarif had invited him previously but he had not taken up the offer "but now I think everything is in place for me to go".
"I find it completely normal that after this historic deal was signed, France and Iran should restart normal relations," he told France Inter radio.
Although he did not give details, his aides later said that the trip would probably take place on Wednesday.
As sanctions are phased out according to the deal's provisions, Western nations hope to rebuild trade ties with Iran.
Gabriel started a three-day visit, in which he was accompanied by representatives of companies and industry groups, on Sunday.
But Fabius said that he will be going as a political representative and will not be accompanied.
Representatives of France's bosses' union, the Medef, are to go in September, he said.
Franco-Iranian trade has fallen from four billion euros in 2004 to 500 million euros in 2013.
A Medef visit to Iran last year was criticised in the US as being too early.
Fabius was reported to have struck a tough stance in the nuclear negotiations but he said that French firms would not suffer because of it.
"In diplomatic life, as in life in general, you never lose anything by being respected," he said.