The Daily Mirror said the Prime Minister gave a speech at a packed leaving do for a senior aide last November when the country was in the midst of the second lockdown.
The newspaper said members of his No 10 team then held their own festive party days before Christmas, while London was under Tier 3 restrictions.
The Mirror on Thursday quoted a Downing Street “insider” who said there were often get-togethers in the evenings while the curbs on freedom were in place.
Ms Rayner has now asked Cabinet Secretary Simon Case to investigate.
In a letter, Ms Rayner said that “the guidance from central Government was very clear that large gatherings and parties were explicitly forbidden”.
She asked if Mr Case was considering referring the matter to the Metropolitan Police, and also asked whether he would be investigating the use of Government property for the gatherings.
She also insinuated it could be a breach of the ministerial code.
On Wednesday, Boris Johnson did not deny the allegations, while No 10 repeatedly argued that “at all stages the rules have been followed”.
Ms Rayner said: “This Government is undermining public health messaging with their actions and we cannot let this go on unchecked.
“It cannot be that the Prime Minister believes there to be a set of rules for the public and a totally different set of rules for himself.”
A Government spokesperson said: “We have received the letter and will respond in due course.”