Judge V M Mohite asked Tiwari to furnish a cash bond of Rs 20,000.
Tiwari's bail application said he had been falsely implicated, and there were several contradictions in the statement of the woman who has accused him of rape.
It pointed out that the woman, who alleges that Tiwari had a sexual relationship with her, is married and has a child.
Tiwari (24), a playback singer, was arrested by the suburban Versova police earlier this month (on May 8) after the woman, allegedly his one-time girlfriend, filed a complaint saying that he raped her repeatedly between October 2012 and December 2013 after promising to marry her, but did not keep the promise.
Tiwari's brother Ankur was also arrested for allegedly threatening the victim.
The singer was booked by the police under sections 376 (rape), 493 (cohabitation caused by a man deceitfully inducing a belief of lawful marriage) and 506 (2) (criminal intimidation) of the Indian Penal Code.
Tiwari is known for the hit song 'Sun Raha Hai Na' from the film 'Aashiqui 2'.