The laws are set to go into effect on August 1, though a legal challenge could postpone them until the matter is sorted out.
This month, Arkansas' legislature passed a bill banning abortions after 12 weeks of pregnancy.
The state's Democratic governor, Mike Beebe, vetoed the bill, but the Arkansas House voted to override the veto.
The Center for Reproductive Rights and the ACLU have vowed to challenge the law in federal court.
Called the Arkansas Human Heartbeat Protection Act, the bill requires testing to determine "whether the fetus that the pregnant woman is carrying possesses a detectible heartbeat."