If an IRB approved a study, does it need to be mentioned in the papers that results from the study?
It depends on the journal. For example, the Journal of Multicultural Counseling and Development instructions for authors state:


  appropriate institutional review board (IRB) review and approval should accompany all studies involving human 
  participants or research material derived from human participants. This information should be clearly stated in 
  the Method section of the manuscript. In addition, the manner in which informed consent was obtained from 
  the study participants (i.e., oral, written, online/electronic) should also be stated in the Method section. If the 
  study was exempted from IRB approval, that information should be indicated in the Method section. Failure 
  to provide this information in the manuscript may result in the manuscript being returned without review.


Nature takes a different approach and does not require the IRB approval to be mentioned in the text (and may not even allow it), but does provide a checklist, that the author must complete and is provide to reviewers, that deals with IRB approval.