Rowley has rejected the allegations and said that he would work towards clearing his name.
The woman, has wished to remain anonymous, told the Scottish Sun the MSP "destroyed" her life after repeatedly sending her abusive text messages and stalking her, saying the abuse has left her "a shadow of the woman I once was".
Mr Rowley has also stepped down as deputy leader of the party, he said in a statement.
SCOTTISH INTERIM LABOUR leader Alex Rowley has stepped down from the role following claims about his conduct, the party has said.
"While that investigation is carried out, I will step aside as deputy leader, as well as Interim Leader, of the Scottish Labour party".
In a statement, he added: "I totally refute these allegations and will take all steps necessary to clear my name".
The news comes as the Scottish Labour leadership contest draws to a close, with either Anas Sarwar or Richard Leanard to be announced as the new party leader on Saturday.
The spokesman said it was not for the party to confirm or deny reports about allegations against party members.
"These allegations must be properly and thoroughly investigated in line with our party's procedures - and I will refer myself to the party so such an investigation can take place".
The 53-year-old has led the party since Kezia Dugdale's resignation.
The father of three grown-up children is described as representing the left-wing of the Labour Party.