The American Civil Liberties Union (ACLU) and Planned Parenthood filed the lawsuit on behalf of abortion providers, who have asked a US federal judge to block the legislation.
The law, which was signed by governor Kay Ivey last week, would make performing an abortion at any stage of pregnancy a crime punishable by up to life in prison for the provider.
The only exception would be when the woman's health is at serious risk.
Unless blocked by a judge, the law is set to come into effect in November.
"Make no mistake, abortion remains - and will remain - safe and legal in Alabama. With this lawsuit, we are seeking a court order to make sure this law never takes effect," said Randall Marshall, executive director of the ACLU of Alabama.
The lawsuit says the criminalising of abortion is clearly unconstitutional and would harm women by forcing them to continue pregnancies against their will.
"For over 46 years, since the Supreme Court decided Roe vs Wade, US law has recognised the fundamental constitutional right to make the profoundly important and personal decision whether or not to terminate a pregnancy," the lawsuit reads.
The plaintiffs in the case are the three Alabama clinics that perform abortions, Planned Parenthood and Dr Yashica Robinson, an obstetrician who also provides abortions at a Huntsville clinic.
Emboldened by new conservatives on the Supreme Court, Alabama is part of a wave of conservative states seeking to mount new legal challenges to Roe vs Wade, the 1973 landmark Supreme Court decision that legalised abortion nationwide.
Governors in Kentucky, Mississippi, Ohio and Georgia have approved bans on abortion once a foetal heartbeat is detected, which can happen as early as the sixth week of pregnancy.
None of the laws have taken effect and all are expected to be blocked by the courts as the legal challenges play out with an ultimate eye on the Supreme Court.
Supporters of the Alabama law have said they expected a lawsuit and expected to initially lose in court, but they hope the appeal could eventually land before the Supreme Court.
"My goal with this bill, and I think all of our goals, is to have Roe vs Wade turned over and that decision ability sent back to the states," Republican representative Terri Collins, the bill's sponsor, said when it passed last week.
Additional reporting by AP