Naomi Blumenthal has refused to answer questions on the scandal after police called her in for questioning last Sunday.
Correspondents say Mr Sharon has been angered by her refusal to co-operate with the police.
Several Likud members have alleged that some candidates for the party's recent internal elections offered bribes to members in exchange for their support.
The issue has damaged Likud's standing in opinion polls ahead of general elections on 28 January.
Hotel bills
The party is heavily tipped to win the election, which would give Mr Sharon another term as prime minister.
But polls are already showing that the affair could cost Likud several seats in parliament.
"
I will not allow Likud members who are said to have been elected in an unlawful way to avoid explanation to the authorities
"
Ariel Sharon
The news agency AFP said Naomi Blumenthal - deputy minister of infrastructure - had been questioned about whether she had paid hotel bills for Likud central committee members in return for their votes.
Mr Sharon had earlier pledged that any Likud member who was tainted by the alleged scandal would be expelled from the party.
In a letter to the deputy minister, quoted by the Israeli daily Ha'aretz, Mr Sharon said: "You made do with an evasive answer through your lawyer and didn't bother to say whether you would ever give an answer to the investigators' questions.
"I will not allow Likud members who are said to have been elected in an unlawful way to avoid explanation to the authorities."
Blumenthal's aide, Michael Karni, said that she had been "shocked" by Mr Sharon's comments and believed she was being made a scapegoat.
Mr Karni said Mr Sharon had not contacted her to hear her side of the story.