Here is the story
My great grandfather was born in 1909, in Ottoman Jerusalem. Born from two german citizens, so he was german as well. In 1914, the Great War starts, and in 1917, Jerusalem falls on British hands. Now, here is the part of the story I have doubts about. My grandfather ,born in my country, tells that the british put great grandfather and his family in concentration camps in Egypt just for being german.
Edit: thanks to user u/canoe_yawl for helping me, I was able to find my great uncle's imprisonment certificate
In addition to the suggestions and information from u/khosikulu, you might also want to search the International Committee of the Red Cross' Archives of the International Prisoners-of-War Agency 1914-1919. They include records for civilian internees, and are free to use. I've made use of this archive to find information on First World War prisoners of war. There is a bit of a learning curve to it, but it is worth trying.
The archive site also includes other relevant records, among them photographs of camps and inspection reports (some of which u/khosikulu has mentioned), that might also be of interest, especially if you've been able to determine where and when your great-grandfather and his family were held.
With a limited ability to do deeper research at present, the TL;DR is 'possibly.' The British did have a number of POW and internment camps in Egypt; two in particular of importance were the Cairo Citadel (mostly women and children captured in the Hejaz, near Mecca, presumably separated from enemy civilians) and the camp of Ras el-Tin, which had men who were interned. The latter camp, reported on at the start of 1917 by the International Committee of the Red Cross (PDF; see 73 in particular, in French) was reported to have particular amenities for Germans and Austrians which strongly indicates that civilians were, or would be, interned there.
Without access to the records of British operations in Egypt, and his name, it would be hard to verify. However, a great many operational records from WWI have been digitized by the UK National Archives, and you might well wish to search through them. However, others, like FO 383/435, which talks about German nationals interned in Alexandria--which would have meant Ras el-Tin, which was about 5 km from the city--are not available online. As to whether German nationals in newly occupied areas like Palestine were sent to established camps in Egypt for processing, all signs point to yes--and their internment would have almost certainly been there, where British control was most direct by mid-war, and transportation from the theater of war would have been easiest.
(e: committee not commission)