"Gopal Valmiki, who is in his late 20s, was apprehended by police in early morning hours," said Colaba police station senior inspector Vinay Gadgil.
The alleged incident had occurred on Monday when the woman was taking a morning walk in the area and the youth allegedly flashed at her, police had said.
She clicked a photo of the youth and posted it online along with tweets about the incident, which went viral on social networking sites.
The victim had also mentioned about two men, who where passing-by and came to her help when she raised an alarm.
The accused has been booked under section 509 (word, gesture or act intended to insult modesty of a woman) of the IPC, Gadgil added.