Muthiah took charge of the Southern Petrochemical Industries Limited (SPIC) on the death of his father Chidambaram in the year 2000.
Muthiah served as the Director of Standard Motors, Tamil Nadu Petroproducts Limited, Southern Petrochemical Industries and SPEL Semiconductor Ltd.
Muthiah was the president of the Federation of Indian Chambers of Commerce and Industry (FICCI) in its Platinum Jubilee year 2003.
He was also conferred the Rotary International District Vocational Services Award for his outstanding efforts in business ethics in the year 1999.
Muthiah is the Managing trustee of MAC (Education) Foundation, a public charitable trust founded by his father Dr. M. A. Chidambaram, which runs the School & College of Nursing in Chennai.