Sila, raised in Germany by conservative Turkish parents, says she fears being "spat at" and "shamed".
Her parents are said to have reacted with "horror" at the 12-page coverage, and her mother has apparently cut off all contact.
Sila, 25 - star of German soap Good Times, Bad Times - claimed the shoot was a reaction to the "slavery" of her youth.
She added: "What I want to say with these photos is, 'Girls, we don't have to live according to the rules imposed upon us'.
"For years I subordinated myself to various societal constraints. The Playboy photo shoot was a total act of liberation."
But Islamic internet sites are being monitored by the BND - the German intelligence agency - after threats were posted about her "shaming Muslim womanhood" and "prostituting herself for money".
One poster on the Jihad Watch website wrote: "She needs to be very careful..." Another simply said: "She must pay."
A kebab shop owner, asked on German TV what he would do if Sila were his daughter, replied: "I would kill her. I really mean that. That doesn't fit with my culture."