Wendy Alexander's campaign for the Scottish Labour leadership broke the law by accepting money from a Jersey-based businessman.
Political reporter, BBC Scotland news website
Her campaign manager, Tom McCabe, accepted there was a clear breach of donation rules when a cheque for £950 was accepted from developer Paul Green.
The MSP who sought the donation, Charlie Gordon, has quit as Labour's transport spokesman at Holyrood.
The party has reported the matter to the Electoral Commission.
During a press conference, Mr McCabe said the incident had cast a shadow over Ms Alexander's leadership campaign and that arrangements were being made to return the money.
It is illegal for people who are based off-shore to donate to a UK political party.
Mr Gordon at first told the campaign team that the money had been donated legitimately through a Glasgow company, Combined Property Services, but it later emerged that Mr Green's name was on the cheque.
Mr Green said that Combined Property Services did work for his companies, but stressed it was completely independent and would have no reason to be aware of the donation.
In a statement, Mr Green also said Mr Gordon had specifically asked him to donate £950 to Ms Alexander's campaign, that he had been told it complied with Electoral Commission rules and that the money came from his personal account.
Mr McCabe, who insisted that the other campaign donations were within the rules, said: "Clearly, at the moment, there's been a breach of the law, as it stands."
The Labour MSP and former Scottish finance minister said the priority now was to co-operate with the Electoral Commission and "right a wrong that has clearly happened".
Mr McCabe described Ms Alexander, who became Scottish Labour leader without the need for a leadership contest, as an honourable person.
He added: "She's clearly very upset that having secured the leadership and having done so successfully, this kind of distraction, I think, casts a shadow over the entire campaign."
Making a statement to journalists, Mr Gordon explained: "I asked for a donation from Mr Green, and he asked me to ensure that it was in line with the rules.
"I handed the donation on to the campaign team and conveyed to them that it was a donation under the auspices of Combined Property Services and that Mr Green had a controlling interest in the company."
The MSP for Glasgow Cathcart went on: "Unfortunately I was wrong in both these assumptions.
"I acted in good faith and I deeply regret the fact that this has happened and that Wendy Alexander has been in any way been implicated."
Mr Gordon said he had apologised to Mr Green for the distress which the situation had caused him, as well as to Ms Alexander, who declined to comment further, and her campaign team.
Mr Green, a well-known Labour supporter, issued his statement in order to "clarify the position further".
It read: "In August of this year I was asked by Mr Gordon to donate £950 to Wendy Alexander's campaign to become leader of the Scottish Labour Party.
Mr McCabe said other donations were within the rules
"I asked Mr Gordon if this complied with the Electoral Commission rules and was told that it did. Relying on that confirmation I made the donation from my personal account."
Mr McCabe said that modern electoral law was now "extremely complex", adding: "It is now very difficult, I think, to raise money for political campaigns and cover all the bases that make sure you're entirely within the law."
The story emerged after revelations that a property developer gave £650,000 to the UK Labour Party through intermediaries, which may breach electoral law.
David Abrahams gave Labour the money over four years under other people's names.
Prime Minister Gordon Brown has described the situation as unlawful and "completely unacceptable".
There were calls from some sections of the SNP for Ms Alexander to consider stepping down as leader, while the Conservatives said the episode was embarrassing for Scottish Labour.
Scottish first minister and Nationalist leader Alex Salmond told BBC Scotland: "I think the Labour Party is in substantial trouble north and south of the border."