Brahimi was the second of two opposition politicians to have been assassinated last year by suspected jihadists as Islamist violence rocked the North African country, which was the birthplace of the Arab Spring revolutions in 2011.
The security forces "surrounded a house (near the capital Tunis) where a terrorist group had holed up. Following a sustained exchange of fire, four elements were arrested," interior ministry spokesperson Mohamed Ali Aroui told AFP.
"Among them is Hmed el-Melki, alias 'Somali,' one of the elements implicated in the assassination of the martyr Mohamed Brahmi," he said.
The announcement came after the government said Tuesday that the suspected Islamist assassin of Chokri Belaid -- the first of the murdered opposition politicians -- had been killed in a police raid.
Also Read
Gunmen killed Belaid on February 6 and Brahmi on July 25, both of them outside their homes.
Authorities blamed the murders on the Ansar Al-Sharia, a jihadist outfit accused of links to Al-Qaeda, but the group never claimed responsibility for those or any other attacks.
Belaid was a charismatic leftist politician and virulent critic of the Islamist party Ennahda then in power. His murder triggered massive anti-government protests and a crisis from which Tunisia has only recently started to emerge.