Makhmudov was jugged on Monday night in Chechnya at the home of his parents after being on the run for years, Russia's federal investigative committee announced on Tuesday.
Makhmudov's brothers, Dzhabrail and Ibragim, and former police officer Sergei Khadzhikurbanov have been investigated for several years over suspected involvement in the killing.
All three were acquitted on a lack of evidence in a jury trial in 2009, but the verdict was annulled by the supreme court and a new investigation reopened with the same suspects.
Politkovskaya, a 48-year-old mother of two who published damning exposes of official corruption and rights abuses, was rubbed out in the stairwell of her Moscow apartment on October 7 2006.
Reporting on abuses
Renowned for her opposition to the Chechen conflict, Politkovskaya also reported on the alleged human rights
...which often intentionally defined so widely as to be meaningless...
abuses of Russian military forces under the leadership of former Russian president Vladimir Putin
...Second President of the Russian Federation and the first to remain sober. Because of constitutionally mandated term limits he is the current Prime Minister of Russia. His sock puppet, Dmitry Medvedev, was installed in the 2008 presidential elections. Putin is credited with bringing political stability and re-establishing something like the rule of law. During his eight years in office Russia's economy bounced back from crisis, seeing GDP increase, poverty decrease and average monthly salaries increase. During his presidency Putin passed into law a series of fundamental reforms, including a flat income tax of 13%, a reduced profits tax, and new land and legal codes. Under Putin, a new group of business magnates controlling significant swathes of Russia's economy has emerged, all of whom have close personal ties to Putin. The old bunch, without close personal ties to Putin, are in jail or in exile.... She also covered alleged abuses by Chechen rebels and the current Moscow-backed administration led by the Kadyrov family in Chechnya.
Her death came as her reporting was increasingly being seen as a threat to the Chechen government, which has been accused of the rampant torture, abduction and murder of opposition figures.