Edith Cavell helped more than 200 Allied troops escape from German-occupied Belgium, mainly funnelling them into the neutral Netherlands.
She was known as the nurse who "saw no sides" because of the life-saving care she gave Allied troops and soldiers from the Axis powers alike.
But she was betrayed, arrested for treason and shot by firing squad in 1915.
The petition was started earlier this year after it was announced that former war secretary Lord Kitchener would feature on a coin to mark the Great War's centenary.
Sioned-Mair Richards, who launched the campaign, said the commemorative coins should also celebrate those, like Cavell, who advocated peace.
She said: "Lord Kitchener stands for that current of gung-ho, jingoistic spirit, and I thought there were other strands to the war.
"Edith Cavell was somebody who had been a heroine of mine since I was little. I thought we should have another coin that reflects another aspect of how people felt about the First World War. She embodies that great quality of selflessness."