Zelenskiy had said on Friday that Ukraine would be forced to act if President Alexander Lukashenko did not remove the stations in two regions bordering Ukraine within a week.
"From June 22, the relay stations have stopped working on the territory of Belarus," Zelenskiy said in an audio message to reporters.
"Whether they took them down or not, honestly, I don't know for now. But we are working on this."
Reuters could not independently verify his assessment.
It was not immediately clear how the stations had stopped working, if that was confirmed or whether there had been an immediate effect of any shutdown.
Zelenskiy has warned in recent months that Russia plans to draw Belarus more deeply into its war in Ukraine.
Russian forces used Belarusian territory to stage their full-scale invasion in February 2022.
Ukrainian drones knocked out power in the biggest city in Russian-held Crimea on Wednesday and targeted facilities in central and southern Russia, local officials said.
Ukraine has intensified strikes on Russian oil refineries, depots and supply routes this year, prompting Russia's parliament on Wednesday to take action to curb growing fuel shortages in many regions.
Fuel issues have been particularly acute on the Crimean peninsula, which Russia seized and annexed in 2014.
The Russian-installed governor of Sevastopol this week mandated early closing for public transport and cafes and said street lights would be dimmed to protect the city during overnight attacks.
