Written by Martha, nine, and her father David, Never Seconds had a run of 2500 which has been snapped up since publication last Thursday.
Martha said: "It's funny to think our book is in lots of people's homes being read and enjoyed now. It's helping lots of children and that's brilliant."
On hearing about the book's sell-out on Twitter, former first minister Jack McConnell tweeted "Hope you are printing more – great story, great cause".
It tells the story of Martha, from Lochgilphead, Argyll who set out to raise funds for the charity Mary's Meals in April with a blog in which she posted daily reviews of the lunches served up at her school, accompanied by a picture of the meal.
She has raised more than £120,000 for children in Malawi and won The Herald's Public Campaigner of the Year 2012.
Six weeks after Martha set up the blog, she was told by Argyll and Bute Council she could no longer take photographs of her lunches as media coverage apparently left catering staff fearing for their jobs.
The ban sparked a barrage of negative publicity for the council, which then backtracked.
A donation of £1 per copy goes to Mary's Meals, which means that around 65,000 people will receive a meal from the charity from the first print-run.
Cargo Publishing say the next print run will rise to 7500.