خاص بالصحافة:
للنشر الفوري

If this is a press release or communique, then the phrase :Press Information" is not essential. The significant part is "for immediate release". So للنشر الفوري may be sufficient in many cases.

Here is an example:

http://www.usaid.gov/press/releases/2003/pr030722_ar.html

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Note added at 14 hrs 5 mins (2003-09-19 10:53:16 GMT)
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Note that this a caption usually placed in the beginning of a press release. An alternative translation can be:

إشعار للصحافة: للنشر الفوري