She made the insult after Chris Clarkson, the MP for Heywood and Middleton in Rochdale, accused Labour politicians of taking an opportunistic approach to the pandemic.
Sources close to Ms Rayner claimed she was shocked by the accusation after she opened the debate by talking about her aunt who died from coronavirus last week.
Mr Clarkson was subjected to the heckle after he suggested that members of the shadow front bench believed the pandemic was a "good crisis" to exploit.
He was forced to interrupt his speech to ask: “Excuse me, did the honourable lady just call me ‘scum’?”
While Ms Rayner was not asked to withdraw her comment in the chamber, deputy speaker Dame Eleanor Laing intervened to scold her.
She said: "From the front bench we do not have remarks like that. Not under any circumstances, no matter how heartfelt it might be. Not at all."
Conservative MPs defeated the Labour bid to force ministers to publish a "clear and fair national criteria" for providing financial support, and after the vote Conservative Katherine Fletcher raised a point of order.
She accused Ms Rayner of having "shamed Manchester” with her remarks and asked: "Is it in order for a senior member of the Labour front bench opposite to repeatedly call out 'scum' when my colleague was talking and then to fail to retract it or apologise?”
Treasury minister Jesse Norman defended the Government's economic response and criticised the language used by Ms Rayner.
He told the Commons: "I don't think it's consistent with the Labour Party's commitment to avoid party politics to have descriptions from the opposite side of, in one phrase, 'screwing people over' heard in this chamber, or referring to a member of this chamber as 'scum' from the Labour front bench."
Sara Britcliffe, the Tory MP for Hyndburn, criticised the deputy leader’s “attitude” and deputy speaker Nigel Evans admitted the language used in the debate had made him "wince".
Mr Clarkson later wrote to Labour’s deputy leader asking her to retract and apologise for the comment “in the interest of providing a united front in the battle against coronavirus”.
Ms Rayner later said in a statement: “I apologise for the language that I used in a heated debate in Parliament earlier.”