Senator Van resigned from the Liberal Party following allegations, which he denies, of inappropriate conduct towards independent senator Lidia Thorpe and former Liberal senator Amanda Stoker.
There are also claims against him from a third unnamed person.
Senate President Sue Lines on Monday revoked the warrant nominating Senator Van to act as a temporary chair of committees when the deputy president and chair of committees was absent.
Senator Van is not expected to attend parliament this sitting week, which is the last to be held until July 31.
Opposition Leader Peter Dutton called for Senator Van to resign from parliament altogether, but the Victorian senator quit the party before a committee could meet to discuss the allegations against him.
Senator Van said in a letter to Victorian Liberal Party president Greg Mirabella he could not remain a member of a party that "tramples upon the very premise on which our justice system is predicated".
"Given the Liberal Party's wholesale disregard for due process and natural justice in relation to allegations made against me, I write to resign my membership effective immediately," he said.
Nationals leader David Littleproud said Senator Van should be afforded the presumption of innocence, but Mr Dutton reserved the right to remove him from the Liberal party room.
"In the Senate there's a clearer case around where senators remove ... themselves voluntarily out of that party and they were elected within that ticket, then they should be replaced with someone from that party," he told ABC Radio on Monday.
Agriculture Minister Murray Watt said the past week in parliament, when the allegations were raised, was distressing.
"They are very serious allegations and (Senator Van) should really seriously consider his position," he said.
"It is a matter for David Van and the Liberal Party as to how they handled these allegations when they were first raised and what efforts were undertaken."
Nationals senator Bridget McKenzie said on Sunday she was aware of rumours in parliament about Senator Van but did not know of the specific claims made against him.
She said the decision by Mr Dutton to immediately expel Senator Van from the party room in the wake of the allegations was the right one.
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