AICTE is approved by the Institutions and University Grants Commission (UGC) approved for any university. 

Sanskrit University is a University and because of which there is no need of AICTE approval, but the university is approved under UGC part 1 and part 2 as well as the university is accredited to all its regulatory body of the courses. 

For example programs like law are accredited to Bar Council of India, Pharmacy is accredited to Pharmacy Council of India, B.Sc. Agriculture is accredited to ICAR, etc. 

Sanskriti University is approved in all, you can check it on the official websites of the authorised bodies.

Therefore, Sanskriti University is approved by all the accrediting bodies and authorities.

Universities do not need any affiliation to AICTE; it is the accrediting body for the institutes. The university should be approved from the University Grants Commission which is mandatory for a registered University. Sanskrit University is approved under UGC.