Police kept a heavy presence at the cemetery but the situation was calm, Russian independent TV channel Dozhd (Rain) reported.
"The police let those wishing to bid farewell to the politician pass through and do not rush anyone," the outlet wrote on the Telegram messaging app, quoting one of its readers on the scene.
Dozhd also reported that "spontaneous memorials" to Navalny had been destroyed in several Russian cities. Flowers were removed in cities including St Petersburg and Voronezh, it said.
Under a heavy police watch, thousands bid farewell to Navalny on Friday after his still-unexplained death two weeks ago in an Arctic penal colony.
The crowds who thronged to honour Navalny outside a church and cemetery in a snowy south-eastern suburb of the capital chanted slogans for him and against Russian President Vladimir Putin and the war in Ukraine.
Police did not act against them, but at least 106 people were detained at events across Russia in Navalny's memory, said OVD-Info, a rights group that tracks political arrests. It said most were stopped while trying to lay flowers at monuments dedicated to victims of Soviet repression.
Navalny was buried after a short Russian Orthodox ceremony, with vast crowds waiting outside the church and then streaming to the fresh grave with flowers.
Navalny's widow, Yulia Navalnaya, was not seen at the funeral. She has vowed to continue his work, and thanked him for "26 years of absolute happiness".
The funeral followed a battle with authorities over the release of his body.
His team said several Moscow churches refused to hold the funeral for the man who crusaded against official corruption and organised massive protests.
Many Western leaders blamed the death on the Mr Putin, an accusation the Kremlin angrily rejected.
