Ms Sturgeon said Anas Sarwar was “brave” to go public with his claim a Labour councillor refused to support his Labour leadership bid because he was a “brown, Muslim Paki”.
Mr Sarwar said he had been “inundated” with examples of everyday racism since revealing the allegation against Davie McLachlan, former leader of the Labour group on South Lanarkshire Council, who denies the claims and has been suspended by Scottish Labour pending an investigation.
Speaking at First Minister’s Questions, Mr Sarwar said: “In the last few days I’ve been inundated with stories of everyday racism and Islamophobia.
“This includes a young woman who had her hijab ripped off her head at an underground station, a child scared to go to school because he is regularly called a terrorist.
“A hotel worker who is regularly racially abused but is told by his employer that the customer comes first.
“A council worker convinced that he missed out on that promotion because of his colour and religion.
“This isn’t about one individual or about one organisation, it is about a culture.”
He called on the First Minister to commit to taking action on issues raised by his cross-party group launched earlier this week on tackling Islamophobia, which she did.
Ms Sturgeon said: “Anas and I are political opponents locally as well as nationally, but I have genuinely admire the way in which he has spoke up this week, the bravery with which he has done it.
“It would be brave in any circumstances but I think all of us know that when we are raising issues that involve people within our own parties that is even more difficult to do, and therefore the praise should be even greater for having done so.”
She added: “Everyday racism, Islamophobia, any form of prejudice and bigotry is unacceptable.
“It’s unacceptable when Anas Sarwar is the subject or the victim of that, or Humza Yousaf, or anybody across our society.”
She said the parliament should be united in tackling racism in all its forms.