He will also take sick leave from his political functions as an MP in the Swiss National Council to follow medical treatment to bring his drinking under control, he said in a statement.
In an article published last Thursday Le Temps revealed that on a night in November Buttet was arrested by police after they were called out by a woman, believed to be Buttet's former lover, who claimed he had been harassing her by standing in her garden insisting to be let in.
According to the paper the married politician had had an affair with the woman – who Le Temps said was also a member of the CVP – and since it ended he had contacted her some 50 times in one day by text, email and phone.
The paper also alleged Buttet had acted inappropriately with several other women – journalists and politicians – in the course of his political activities in Bern.
Buttet acknowledged the claims, saying he had gone through a marital crisis which had affected his judgement and behaviour. According to him, his inappropriate acts in Bern happened in the evenings when he was under the influence of alcohol.
Buttet was suspended from his post as vice-president of the party last week but initially ruled out resigning, admitting he had acted badly but denying he was a ‘harasser'.
But on Monday he handed in his resignation to the CVP president, saying in a statement that he offered his “deep apologies to my wife, my family and those who have been hurt by my inappropriate behaviour, including my party colleagues”.
He said he would seek treatment for alcoholism and would only after that discuss his political future with his party.
“Until further notice I withdraw from my elected functions,” he said.
The CVP said Buttet's behaviour had been “unacceptable”, and that it would enter into discussions about his political future as soon as possible.
Speaking to the press, Serge Metrailler, president of the Valais branch of the party, welcomed Buttet's willingness to seek treatment and said it was important that he “finds the answers to real questions”.
No one will replace Buttet in the Swiss National Council – the lower house of parliament – during his sick leave.
The issue of whether he should also resign from his elected role will be discussed in the coming days, according to the Swiss press.
In an editorial, Le Temps said it was unlikely Buttet, described as he CVP's “prodigal son”, could come back to parliament after his treatment.
By taking sick leave Buttet had a clear strategy, said the paper: “to let the storm pass and come back to Bern as soon as possible”.
But that is not very realistic, it added, with one CVP politician telling the paper that Buttet's political credibility was ruined.
Swiss president Doris Leuthard told broadcaster RTS that behaviour like Buttet's was “unacceptable for politics”.
Meanwhile the Valais public prosecutor has opened an investigation regarding the leaking to the press of Buttet's arrest, saying it had likely come from someone in the police or public prosecutor's office.