Is cousin marriage illegal in India?

Partly. Cousin marriage is restricted in India. Civil marriage law bars first cousins unless a custom allows it.

Special Marriage Act 1954 First Schedule lists all first cousins as prohibited; s.4(d) proviso lets the marriage go ahead where a custom governing one party permits it (Hindu Marriage Act s.5(iv) similar). Rules depend on the law the couple marries under, so not one nationwide ban.

Source: Special Marriage Act 1954

Banned (17)Restricted (8)Allowed

India is one of 17 countries where cousin marriage is banned, and 8 more restrict it.
Its neighbours: banned in 1 of 6 (China).
In Asia: banned in 6 of 46 countries.