The couple became husband and wife during a week of "quite hectic" celebrations in New Delhi, attended by 1,000 guests.
Nayyar, who plays Raj Koothrappali in The Big Bang Theory, first met the former Miss India three years ago.
"She unlocked something in me that I had never felt before," he recalled to People.
Nayyar's co-stars Kaley Cuoco, Jim Parsons, Johnny Galecki and Simon Helberg were apparently unable to attend the celebrations.
His marriage comes days after Cuoco confirmed that she is no longer engaged to boyfriend Josh Resnik.
Helberg, meanwhile, announced in late January that his wife Jocelyn Towne is pregnant with their first child.
Watch Kunal Nayyar in a clip from The Big Bang Theory below: