"I informed MK Oren Hazan this morning that for the time being I won't be able to let him run the plenum sessions as deputy speaker of the Knesset, in light of the report on him on Channel 2," Edelstein wrote on Facebook.
"I am full of hope that he will clear himself of all suspicions, and I will be happy to apologise to him. But in the current public atmosphere, ethically -- even if not criminally -- there is no way he can run the plenum."
Hazan, a member of Prime Minister Benjamin Netanyahu's Likud party elected into parliament on March, denied in a series of interviews on Tuesday any misdoings.
His lawyer also told military radio Hazan had a medical condition that prevented him from being able to use hard drugs.
Following Edelstein's announcement, a furious Hazan phoned the Knesset speaker and threatened to dig up dirt on him and expose it publicly, an aide to Edelstein told AFP.