Jeremy Meeks, 30, was one of four men arrested in raids in Stockton, California following a series of shootings and robberies.
After his picture was posted on the Internet by police it quickly attracted 30,000 “likes” on Facebook and nearly 10,000 comments, mostly from women.
Many referred to Meeks’ blue eyes and prominent cheekbones.
Comments included “I’m in love with a criminal”, “Can we be handcuffed together?” and “He can kidnap me any day”.
Another said: “Why is he breaking the law when he should be making millions modelling?”
Some women suggested Meeks apply for a spot on the reality television show America’s Next Top Model when he gets out of jail.
Meeks was arrested in a police operation to curb violence in Stockton, a city of 300,000 people in northern California, which declared bankruptcy two years ago.
Four guns were found in the raids which involved the FBI and US Marshals.
Stockton Police Department spokesman Joseph Silva said Meeks was “one of the most violent criminals in the Stockton area” and was arrested on five weapons charges and one gang charge.
Meeks, who is being held on $900,000 bail, is due to appear in court on Friday afternoon.
The other three men arrested, whose mugshots also appear on the Stockton Police Facebook page, gained less than 20 comments between them.