The posters were spotted attached to lamposts and drainpipes across the city over the weekend.
Deputy First Minister John Swinney, who is also MSP for Perthshire North, criticised the stickers on Twitter: "This is atrocious and has no place in Perth or any other part of our country.
"We must stand together to resist this unacceptable material."
Police Scotland said it was "currently looking into the matter."
The posters have outraged local campaign group Perth Against Racism.
In a Facebook post, the group said the slogan had been used by far right, white supremacist groups in the USA and voiced concerns that persons of colour would be affected by the signs.
Perth Against Racism said: "We are so sad and angry that even one Perth resident has been made to feel like this.
"Let's get these down folks. Show that we are a welcoming and diverse city. I have seen quite a lot ripped off already.
"We ask this person to come forward and talk about their motivation.