Ukrainian officials have posted video saying it shows Ivan Fedorov being led away blindfolded on Friday.
In a message, President Volodymyr Zelensky accused the Russians of “moving to a new stage of terror”.
Melitopol, a small city in south-eastern Ukraine, was one of the first to fall to the Russians.
Russia invaded Ukraine on 24 February, arguing it felt threatened by a neighbour intent on joining Western-led organisations such as the Nato military alliance.
In his message late on Friday, Mr Zelensky called Mr Fedorov a “mayor who bravely defends Ukraine and the members of his community”.
“They have moved to a new stage of terror in which they are trying to physically eliminate representatives of legitimate local Ukrainian authorities.”
Mr Fedorov told the BBC days ago that his administration was not going to co-operate with the Russians “in any way”.
There have been protests in Melitopol every day since the Russian occupation.
On Saturday, hundreds surrounded the administration building demanding the mayor’s release.
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