The 61-year-old said security officials had prevented him from boarding a flight from Rabat airport to take part in a cultural event in Spain.
“It’s a flagrant violation of the law,” he said, adding that Moroccan legislation only allows a travel ban to last for one year.
He said he had started a 48-hour hunger strike in response.
Moroccan authorities could not be reached for comment.
Known for his criticism of the authorities, Monjib was sentenced in January last year to 12 months in prison, after a trial opened in 2015 and was repeatedly postponed.
He is accused of embezzling funds at a center he founded to support investigative journalism.
Monjib has repeatedly denounced his “wrongful arrest” and has denied the charges against him, while the center’s donators have never lodged complaints against him.
The historian is also under investigation for alleged money laundering, in a case that saw him provisionally detained for three months until March 23 last year, when he was released following a hunger strike.
An appeal hearing is expected on December 29.
Monjib says he is being targeted for criticizing Moroccan intelligence services over the alleged repression of opposition figures.
Several journalists critical of Morocco’s government have been imprisoned in recent years for sex crimes, accusations they have denied.
Morocco stands at 135 out of 180 in the Paris-based watchdog Reporters Without Borders (RSF) world press freedom ranking of countries.