The complaint from backbench Conservative MP David Davies to the Parliamentary Commissioner for Standards could lead to an inquiry into Hain's conduct.
Davies told BBC television there had been a "very clear breach of the rules."
Work and Pensions Secretary Hain said in November he had failed to register with the electoral watchdog a 5,000-pound donation to his unsuccessful campaign last year to become the Labour Party's deputy leader because of an administrative error.
But on Thursday he admitted his campaign had failed to declare donations totalling more than 103,000 pounds within the time frame required by electoral rules.
He said he met the Electoral Commission on Thursday and provided full details of the donations.
He had been concentrating on his ministerial duties, relying on campaign officials to comply with election rules.
"I very much regret that these reports were not made on time. I should have given higher personal priority to the day-to-day administration and organisation of my campaign," he added in a statement.
Hain said all the donations had come from people who were legally entitled to donate to his campaign, including friends, trade unions and business people.
The Guardian said Hain's revelations mean that in all he spent 185,000 pounds on his failed campaign. Anyone who receives donations of more than 1,000 pounds is supposed to declare the amounts to the Electoral Commission.
In an interview with the paper, Hain said there had been "serious organisational and administrative problems".
"I was not watching my back and unfortunately it appears others were not either," he said.
The Conservatives and Liberal Democrats said the failure to declare the money was an "extraordinary" oversight.
"How on earth did he manage to get this so dramatically wrong?" asked Chris Grayling, the Tory spokesman on Work and Pensions. "After the events of the past two months, it looks as if he and his senior colleagues have a complete disregard for the rules."
Plaid Cymru Parliamentary Leader Elfyn Llwyd said Hain should resign. "His position is untenable," Llwyd told BBC television.
But Gordon Brown's spokesman said the Prime Minister had "full confidence" in Hain.
Hain's disclosure is an embarrassment for Brown, whose first six months as prime minister were overshadowed by a party funding scandal and government blunders that have left Labour trailing in opinion polls.
Labour's general secretary resigned and police were called in to investigate last year after it emerged property developer David Abrahams had given more than 600,000 pounds to the party through go-betweens in apparent violation of electoral law.
