The criminal court in Manama ordered Rajab's release from custody but barred him from leaving the country, setting the next hearing in his trial to January 20, the source told AFP, requesting anonymity.
Rajab, a member of Bahrain's Shiite majority, which has been protesting against the Gulf kingdom's Sunni rulers since 2011, was arrested on October 1 after posting comments on Twitter about the interior and defence ministries.
In one of the tweets that were deemed offensive, Rajab charged that many of the Bahrainis fighting with jihadists in Syria were former security forces personnel who had developed Sunni extremist views during their service.
Signup to our newsletter and follow us on Facebook and Twitter!
Rajab's lawyer, Jalila al-Sayyed, used Sunday's hearing to call for her client to be freed, according to the judicial source.
The trial has been condemned by advocacy groups, including Human Rights Watch, which also called for the charges against Rajab to be dropped.
Rajab is the director of the Bahrain Centre for Human Rights and was freed in May after serving two years in jail for taking part in unauthorised protests.
He had led anti-government marches following a bloody crackdown on Shiite-led demonstrations against the Al-Khalifa ruling family in March 2011.