The text messages were sent in a harassing manner, police said, and a countdown was "initiated for the victim to send the male money or consequences would be had."
The man repeatedly threatened harm on the victim if she did not comply, police said.
Milford police received the complaint at 12:15 p.m. Saturday, May 20.
The man, identified as Matthew Mannix of 300 Riversville Road, Greenwich, was taken into custody later that day by Milford Police.
Mannix is charged first-degree criminal attempt/larceny by extortion, second-degree threatening and second-degree harassment.
He was held on $10,000 bond to appear in Milford Court on Monday, May 22.
Click here to follow Daily Voice Greenwich and receive free news updates.