Economist Dr Tim Rideout was suspended from the SNP following accusations of racism sparked by an attack on Ms Patel.
Addressing the comments made by the shamed SNP former member, Conservative MSP Pam Gosal said such comments “have no place in society, let alone in political debate”.
Ms Gosal said she welcomed the SNP taking “quick action” in suspending and launching an investigation into Dr Rideout’s conduct.
However, she said this was not an “isolated incident” and all parties must condemn racism.
Ms Gosal called on the First Minister to continue to “root out and condemn toxic, racist political discourse”.
Ms Sturgeon promised to do so as she said the “individual concerned” was “immediately suspended from the party”, adding that it “would be wrong” for her to comment further.
The First Minister said: "I represent the most diverse constituency of Scotland in this Parliament. I represent the biggest BAME communities in the country.
"I understand these issues and how serious it is that all parties take these issues very seriously and I am absolutely committed to doing so.
"I think this is an issue for all parties. We all have to be prepared to act when necessary in a way that aligns with what we say around these things.
"I am determined that my party does so and I would call on other parties to make sure they always follow suit as well and that is something hopefully we can unite on.”
Dr Rideout, a Lothians member of the SNP policy development committee, replied to a post about remarks Ms Patel made, citing concerns over a potential backdoor for Ukrainian refugees entering the UK from Ireland.
The post read: "Taoiseach Micheal Martin has confirmed that Priti Patel complained to the Irish government that Ireland’s welcoming policy towards Ukrainian refugees would allow them to reach the UK by the back door."
Rideout replied: "So how do we send this person back to Uganda? Clearly hasn't a shred of humanity. Mind you, maybe the new proposed refugee centre on St Helena might avoid inflicting her on anyone. Can compare notes with Napoleon's ghost."