At business questions in the Commons on Wednesday, Anum Qaisar-Javed (Airdrie and Shotts) read out the offensive comments she had experienced as she called for "real action".
Commons leader Jacob Rees-Mogg branded the abuse "appalling", urging the perpetrators to "crawl back under the rock from which they came".
But he said: "I'm sorry that [she] wishes to make this party political because I really think it isn't."
Ms Qaisar-Javed had said: "I'd like to make the House aware that I'm going to quote some offensive remarks and that Mr Speaker has been given advance sight of this question.
"On social media I've been told that I shouldn't be involved in politics because I'm not a Brit, I'm a Paki. That is, of course, wrong on both accounts. I'm neither a Brit nor a Paki, I'm a proud Scot.
"On social media, I've also been told to f*** off home. That, of course, doesn't make sense.
"I was born in Edinburgh, Scotland is my home. I'm not unique, however, in any sense, and we saw this with the horrific racial abuse that black England players received on social media.
"Every day people are racially abused online because of a false narrative built upon prejudice and assumptions. One that ministers in this government have encouraged, I'm afraid to say.
"Yesterday the Prime Minister admitted that there's a systematic issue of racism particularly on social media. The House may be united against racism but we need to see real action. What does the government intend to do about this?
"There was an urgent question yesterday. Will the leader of the House make time for an urgent debate next week in this chamber, [so] MPs of colour can also raise their contributions?"
Mr Rees-Mogg replied: "May I begin by saying how appalling it is that [she] has been treated in that way and anyone who has sent her a message of that kind should – to use the Prime Minister's words – crawl back under the rock from which they came.
"They are not people who should behave in this way and there is one fundamental thing that we should all know, that in this country there is a fundamental equality in every respect of every single British citizen, whether it is somebody who has received a British passport a minute ago, or who has been descended from people who were Picts."
Mr Rees-Mogg branded social media a "sewer that is in need of cleansing".
He said: "I'm sorry that [she] wishes to make this party political because I really think it isn't.
"I think ... the whole House is outraged by the way that she has been treated and there is action being taken, as the Prime Minister set out yesterday. He had discussions with the social media companies to remind them of their responsibilities and of what will happen under the Online Safety Bill if they do not live up to their responsibilities.
"Social media is regrettably a sewer and some of the most disgusting bits of life get washed through it, but it is a sewer that is in need of cleansing."