The Sunni cleric is among 200 individuals wanted in connection with their alleged role in clashes that have left 30 people dead in recent weeks, BBC reports.
Before disappearing, Bakri dismissed the authorities' claims as "unjust".
He settled in Tripoli after leaving the UK, where he lived for 20 years, in 2005 and being banned from returning.
Bakri was often accused of links with al-Qaeda, which he denied.
The Lebanese authorities said the cleric, who was born in Syria and also holds Lebanese nationality, was wanted on charges relating to endangering national security.
He is being sought by security forces in Tripoli as they crack down on those involved in the deadly clashes between the Sunni majority and minority Alawite community in the northern city.
The two communities are deeply divided over the war in neighboring Syria, where they back different sides.
The Lebanese army said it had arrested 75 people during Tuesday's operation in Tripoli, which saw troops moving into the main conflict areas - the Sunni district of Bab al-Tabbana and the neighboring Alawite district of Jabal Mohsen - to try to quell the clashes.
But when the soldiers stormed Bakri's house in the city center, they found that he had already fled. His wife told local media that she did not know where he was.
BBC correspondent says he was one of the best-known radical Islamist preachers in London for years.
After moving to Tripoli, he accused the UK government of spending hundreds of thousands of pounds to keep him under surveillance there.
HH/HH