By Lisa Respers France, CNN

(CNN) -- Alyssa Milano is leading the charge in Hollywood against a controversial bill in Georgia.

House Bill 481, known as the Living Infants Fairness and Equality Act, was approved by state's legislature on Friday and bans abortions after a fetal heartbeat is detected -- as early as six weeks into pregnancy.

Gov. Brian Kemp, a Republican, supports the legislation and is expected to sign it.

Currently women in Georgia are allowed to undergo the procedure up to their 20th week of pregnancy.

Milano penned an open letter to Georgia House Speaker David Ralston and Gov. Brian Kemp against the so-called heartbeat abortion bill.

Dozens of other celebrities including Amy Schumer, Sean Penn, Alec Baldwin, Don Cheadle, Rosie O'Donnell, Patton Oswalt, Sarah Silverman and Mia Farrow signed the letter in support.

"This dangerous and deeply-flawed bill mimics many others which have already been deemed unconstitutional," said the letter, a copy of which Milano tweeted Thursday. "As men who identify as small-government conservatives, we remind you that government is never bigger than when it is inside a woman's body or in her doctor's office."

Georgia is the site of multiple film and television productions, and the letter threatens a boycott if the bill becomes state law.

"We want to stay in Georgia. We want to continue to support the wonderful people, businesses, and communities we have come to love in the Peach State," the letter says. "But we will not do so silently, and we will do everything in our power to move our industry to a safer state for women if H.B. 481 becomes law."

The Writers Guild of America released a statement Tuesday saying passage of such legislation might cause Georgia to lose Hollywood productions.

"This law would make Georgia an inhospitable place for those in the film and television industry to work, including our members," the writers' union said in its statement. "If the Georgia Legislature and Governor Kemp make HB 481 law, it is entirely possible that many of those in our industry will either want to leave the state or decide not to bring productions there. Such is the potential cost of a blatant attack on every woman's right to control her own body."