Rowley has stepped aside from the role of Scottish Labour's interim leader while under investigation
The Scottish Labour Party confirmed he would "stand aside" after a former partner told the Scottish Sun newspaper that their relationship "felt like emotional blackmail and abuse".
It is understood that Mr Rowley, who was election agent for former prime minister Gordon Brown and is MSP for Mid Scotland and Fife, denies the allegations.
Mr Rowley, who had been Scottish Labour's deputy leader, stepped up to take charge of the party after Kezia Dugdale dramatically quit as leader in August.
The woman who made the allegations claimed he made her life "hell with his behaviour" and said she had been inspired to speak out after a number of other women made complaints about misconduct by politicians at Westminster and Holyrood.
Alex Rowley replaced Kezia Dugdale as leader of the Scottish Labour party on a temporary basis
SNP MSP Mark McDonald left the Scottish Government over "inappropriate" behaviour.
But Mr Rowley is the most senior person in the Labour Party to be affected by allegations over conduct.
Voting is under way in the contest to find a new Scottish Labour leader, with the results due to be announced on Saturday.
SNP MSP Mark McDonald left the Scottish Government over 'inappropriate' behaviour
Left-wing MSP Richard Leonard, a former trade union organiser, is running against the more moderate MSP Anas Sarwar – Labour's health spokesman at Holyrood.
Ms Dugdale was the third Scottish Labour leader to resign in the last three years, after her predecessors Jim Murphy and Johann Lamont.
A Scottish Labour Party spokesman said: "Alex Rowley has stood aside as interim and deputy leader of Scottish Labour and referred himself to the Party's internal complaints procedure regarding allegations made against him."
- WATCH: Scottish Parliament erupts as Tory MSP shames Nicola Sturgeon
- Ruth Davidson criticises SNP over ‘unheeded’ 999 calls
- Nicola Sturgeon rejects calls for Mark McDonald to quit as MSP