Parashar has been elected Fellow of AAAS, ACM and IEEE for his contributions to high-performance parallel and distributed computing and has received numerous awards and recognitions for his research and development activities and their impact. These include best paper, poster, presentation award at conferences such as AAAI, SC (paper and poster awards), CCGrid (SCALE award), Australian Computer Society (ACS) (best published paper in 2006), UCC Cloud Challenge award, etc., a R&D 100 Award for the DataSpaces software framework, and multiple IBM faculty awards. He also received an NSF Career award and the Enrico Fermi Award for Argonne National Laboratory.

At Rutgers, Parashar has received the University Board of Trustees Award for Excellence in Research, Peter D. Cherasia Faculty Scholar Award from the School of Engineering, and awards for research, mentoring and outreach from the department and the faculty and students.

Parashar has also received multiple honors from professional societies for his leadership and service including the IEEE T&C Distinguished Leadership Award, IEEE Computer Society Golden Core award, outstanding leadership, and service awards from various IEEE societies such as TCPP and TCSC.