Labour MSP Anas Sarwar is also calling for a review of the legal framework surrounding racist and Islamophobic abuse on social media in a letter to the First Minister.
Mr Sarwar recently claimed that senior Labour councillor Davie McLachlan made racist comments during a conversation between the pair during the recent Labour leadership contest, when the Glasgow MSP lost out to Richard Leonard. This was "categorically denied" by the councillor and a party probe is now underway.
In his letter to Nicola Sturgeon, Mr Sarwar said his proposals were about "challenging a culture that impacts on workplaces, colleges, university campuses and playgrounds across the country".
Mr Sarwar, one of only four BAME MSPs to have ever sat at Holyrood, said: "I want to repeat what I have said in every conversation, in every piece of communication, and in every media comment - this isn't about one individual or one party or organisation.
"It's about challenging a culture that impacts on workplaces, colleges, university campuses and playgrounds across the country," he said.
"What I have set out are steps that I believe the Scottish Government should take to challenge the consequences of everyday racism and Islamophobia.
"This would demonstrate to the public how seriously we - as a Parliament and a country - take this issue and help us to tackle this culture head-on."
He added: "We will consider the points raised by Mr Sarwar when we receive the letter and reply to him in due course.
"Everyday racism, Islamophobia or any form of prejudice and bigotry is completely unacceptable, and it is wrong for MSPs, or anyone in our society, to be the subject or victim of it.
"We are resolved to do everything that it takes to ensure that Scotland is a place where there is zero tolerance of racism in any form."