"The man, Akbar Raj, has confessed to the crime," Raman Srivastava, police chief of southern Kerala state, told reporters in state capital Thiruvananthapuram.
The investigation had not revealed the man was linked to terrorist groups, he said, without revealing his motive for the threat.
Police tracked him through an Internet cafe he had used several days ago.
Singh is due to visit Kerala on Wednesday to celebrate the golden jubilee of the state's founding.

Copyright AFP (Agence France-Presse), 2006