Yes there really IS one!
And, moreover, there is an "Islamic World Heritage Committee" and even a "List of Islamic World Heritage in danger".
This all operates under the auspices of "ISESCO" ("Islamic Educational, Scientific and Cultural Organisation"). This organisation has been in existence since 1982 but its foray into "Islamic World Heritage" seems somewhat newer with the "Islamic World Heritage Committee" having first met in 2010 in Rabat and then in the subsequent 3 years - Cairo, Tunis, Sanaa. I can't find any reference to a meeting in 2014, perhaps the countries involved have had other things to worry about!!
I have tried to find out which "sites" have been inscribed but the information is a bit confusing
a. The ISESCO Web site identifies 5 inscribed sites in Palestine, Egypt, Mali, iraq and Iraq here up to and including 2013 - http://www.isesco.org.ma/templates/isesco/patrimoine_islamique/en/list_en1.pdf
b. But several other Web sites in 2013 list 3 others - St Catherines, Abu Mena and part of Historic Cairo .
i. The Cairo Post - http://www.thecairopost.com/news/31843/news/isesco-enlists-three-egyptian-sites
ii. A Russian Orthodox Christian Web site http://www.pravoslavie.ru/english/65734.htmhttp://www.thecairopost.com/news/31843/news/isesco-enlists-three-egyptian-sites
Quite what UNESCO itself thinks of all this isn't clear. The ISESCO Web site tries to claim that it is all being done in cooperation with UNESCO " The Islamic World Heritage Committee is operating in concert with the World Heritage Committee and the Arab Heritage Committee to propose the appropriate mechanisms and coordinate common positions in order:
To inscribe cultural archaeological sites of the Member States on the Islamic World Heritage List regardless of the civilization and the period to which they belong;
To preserve historical monuments and natural reserves in the Member States;
To safeguard and promote intangible cultural heritage;
To provide emergency assistance for the protection of archaeological sites damaged by natural disasters;
To provide legal support to recover looted cultural property;
To combat illicit trafficking in cultural property;
To offer expertise and technical support for inventorying cultural heritage and ensuring good governance in the field of cultural heritage;
To support Member States' competent authorities to inscribe their archaeological sites on UNESCO World Heritage List;
To prepare reports on the situation of Islamic cultural heritage."
It is also made "clear" that the intention isn't solely to deal with "Islamic" sites but with all heritage "in the Islamic world" -"The name of this committee brings us to give a succinct definition of Islamic heritage. This incorporates the Member States' heritage existing within their territories, including the heritage dating back to pre-Islamic civilizations. Indeed, Member States are entrusted with and responsible for its preservation, being part of Islamic heritage. In this regard, the world states have preserved this heritage throughout the ages, and numerous ancient civilizational landmarks have been preserved and integrated by Islamic civilization. Furthermore, this designation does not suggest that Islamic heritage is limited only to the part produced by the civilization of Islam. It also incorporates all stages and civilizations of the human heritage existing in the Islamic world."
The ISESCO web site provides more information and this link leads directly to the "World Heritage" part of the site - http://www.isesco.org.ma/index.php?option=com_k2&view=item&layout=item&id=75&Itemid=1 04&lang=en#