Rajab, who was present at Tuesday's hearing, is charged with spreading "rumours and false news" via televised interviews in 2014 and 2015 in which he criticised authorities.
The next hearing in Rajab's case is scheduled for April 16. The presiding judge also denied his lawyer's request for release on bail, the judicial source said.
Tuesday was the fourth suspension in Rajab's trial, which opened in January.
The high-profile activist, and founder of the non-governmental Bahrain Centre for Human Rights, also faces a separate trial for a series of tweets deemed "insulting" to Saudi Arabia which has also been postponed multiple times. The next hearing in that case is scheduled for March 22.
Rights groups including Amnesty International have called for authorities to release Rajab on the grounds that he is a prisoner of conscience. Amnesty also called the postponement of Rajab’s trial as blatant harassment.
“Bahraini authorities must stop playing games with Nabeel Rajab’s freedom. He has been arrested and released repeatedly over the past five years and has been banned from leaving the country," said Samah Hadid, Deputy Director of Campaigns at Amnesty International’s Regional office in Beirut.
"By postponing his trial... they are cruelly stringing him along as punishment for his peaceful activism. Their refusal to release him from custody in December despite a court order suggests this is part of a deliberate strategy to harass him.
"Instead of flouting his rights to freedom of expression and depriving him of his liberty they should end this campaign of harassment, immediately and unconditionally release him and drop all the charges against him,” Hadid added.
Rajab, who had been pardoned for health reasons in 2015, was rearrested in June and is on trial on a list of charges, including insulting a state institution and Saudi Arabia in online postings.
A Bahraini court had last month ordered Rajab freed pending the trial on charges of spreading false information. But the prosecution decided to keep Rajab in custody pending questioning in another cyber crime case on a similar charge of "spreading false news about the situation in the kingdom".
Rajab has been repeatedly detained for organising protests and publishing tweets deemed insulting to Bahrain's Sunni authorities.
He previously served two years in jail on charges of taking part in unauthorised protests in the Shia-majority kingdom.