But the court acquitted him of the more serious charge of seeking to overthrow the monarchy and change the political system, the source added.
Salman, 49, was also found guilty of "insulting an official body," the source said, referring to the interior ministry.
His arrest on December 28 drew condemnation from both the United States and Iran, as well as human rights groups.
It also triggered demonstrations across the kingdom.
Salman was present for the verdict, which was delivered amid tight security outside the Manama court, witnesses said.
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"Today's verdict against Ali Salman drives Bahrain deeper into political crisis," said Brian Dooley, head of Human Rights Defenders Programme at the Washington-based Human Rights First.
"Sending the leader of the main opposition group to jail for peaceful protests only encourages those pushing for violent change, and it sweeps any chance of a negotiated settlement off the table," he said.
Tiny but strategic Bahrain, which is home to the US Navy's Fifth Fleet, has been rocked by unrest since a 2011 Shiite-led uprising demanding a constitutional monarchy and more representative government.
Salman heads the Al-Wefaq Shiite political association, which held the largest parliamentary bloc until its 18 MPs walked out in February 2011 to protest violence used against demonstrators.
Despite the crackdown, protesters continue to frequently clash with security forces in Shiite villages outside Manama.
At least 89 people have been killed in clashes with security forces since 2011, while hundreds have been arrested and put on trial, rights groups say.