Salameh, a Hamas leader, is serving multiple life sentences over his alleged role in a series of attacks carried in 1996.
In the video, Ben-Gvir is seen threatening Salameh, though the source does not provide further details about when or where the footage was recorded.
Hamas condemned the remarks, describing Ben-Gvir's actions as “provocative” and saying they constitute a “flagrant violation of all international laws”.
The Palestinian movement said the video would not affect the resolve of Salameh or other Palestinian prisoners held in Israeli jails.
“We have exerted – and will continue to exert – every possible effort at all levels and through all means to secure the release of our prisoners from the occupation’s jails,” Hamas said in a statement.
“We remain committed to this pledge until they attain their freedom.”
Hamas also issued a direct warning to Ben-Gvir, saying: “The fate of Ben-Gvir and his ilk – leaders of the fascist entity – will be the same as that of other war criminals throughout history.”