The 2014 Eurovision Song Contest winner had been due to perform with her trio Basalt on Friday evening at an event celebrating multicultural collaborations between European artists and immigrants.
But British authorities refused to grant UK entry to the three Syrians, who have been living in Vienna for more than two years after fleeing the bloody civil war in their homeland.
"Due to the unfortunate fact that my friends Amjad, Noor and Almonther from Basalt were unsuccessful in their visa application to enter the UK. I am not performing at the Edinburgh International Festival tonight," Conchita, 28, wrote on her Facebook page on Friday.
"We are all very sorry as we were looking forward to being there."
Conchita and Basalt had been scheduled to perform their song 'Small House' – sung in English and Arabic – as part of the New European Songbook, a Europe-wide initiative of the Edinburgh festival.
The project "is about how different people affect and enrich the cultural geography of the places they come to", festival director Fergus Linehan told AFP.
"The symbolism (of the visa denial) is awful… It's particularly frustrating because of the whole point of the concert."
Linehan said he had extended an "open invitation" to Basalt to come and perform at a later stage.
The annual Edinburgh festival, which celebrates its 70th edition this year, is the largest arts festival in the world.
The three-week cultural smorgasbord of opera, dance, music and theatre runs until August 28th.