Mr Zarif, a fluent English speaker who originally joined Facebook in 2009 - is the most popular minister on the site, with 160,000 likes.
By contrast, the government's page - opened on August 30 and titled Webpage of the Government of Wisdom and Hope - currently has around 3,000 likes.
Among its latest posts is a pledge to compensate people with acute diseases for high medicine costs by opening talks with health insurance companies.
Abbas Akhundi, the roads minister, promises on his page to make building a new motorway from Tehran to the north of the country a priority to ease traffic congestion.
Mr Rouhani, a comparatively moderate cleric, vowed to ease internet censorship during his election campaign, during which he lamented Iran's "security atmosphere".
The use of social media by senior officials is not unprecedented, despite the legal prohibitions existing for ordinary Iranians. Facebook, Twitter and Instagram accounts are held in the name of Ayatollah Ali Khamenei, the supreme leader, and are thought to be run with his consent.
Facebook and Twitter were officially banned following the upheavals that greeted Mr Ahmadinejad's bitterly disputed re-election in 2009, when opposition activists tried to use them to organise demonstrations.