There is nothing in the official brochure of AIIMS PG explicitly about it. But as per NEET PG brochure for instance say about the matter-

"Indian citizens or overseas citizens of India who have obtained their Primary Medical Qualifications from Medical Colleges outside India should have qualified the Foreign Medical Graduate Examination(Screening Test) which is conducted by National Board of Examinations. Further, they should have been registered with MCI/SMC and should have completed their internship or likely to complete their internship on or before 31.03.2018.
Foreign Medical Graduates are required to bring their FMGE Pass certificate issued by NBE on their testing day.

As per that you should also be eligible for AIIMS PG if you meet the other criteria. As per regulations of MCI for PG admission Every student, selected for admission to a Post Graduate medical course in any of the medical institutions on acquiring MBBS Degree or an equivalent qualification there to shall have obtained permanent registration with the Medical Council of India, or any of the State Medical Council(s) or shall obtain the same within a period of one month from the date of your admission.

Good Luck!

Students must have completed MBbS or BDS from reputed Institute by MCI and one must have 1year rotary internship experience and minimum 55. 0%aggregate marks in graduation for eligibility.

https://medicine.careers360.com/articles/aiims-pg-eligibility-criteria