The Republican-led Senate approved the legislation 24-10. It needs at least another vote of approval in the House of Representatives, which is also led by Republicans, before it can head to Republican Gov. Mike Parson's desk.
The bill includes exceptions for medical emergencies — but not for pregnancies caused by rape or incest. Doctors who perform abortions after eight weeks face five to 15 years in prison.
Parson, who supports the bill, has said he believes this gives Missouri the opportunity to be "one of the strongest pro-life states in the country."
Senate Democrats, including Sen. Jill Schupp, of the St. Louis area, attacked the bill on Wednesday.
"Much of this bill is just shaming women into some kind of complacency that says we are vessels of pregnancy rather than understanding that women's lives all hold different stories," Schupp said.
"We cannot paint with a broad brush and interfere by putting a law forward that tells them what they can and cannot do," she added.
The Missouri bill comes as abortion opponents across the country push for new restrictions, hoping that the conservative-leaning U.S. Supreme Court will overturn Roe v. Wade, its landmark 1973 ruling that legalized abortion.
Hours before the Missouri state Senate passed the legislation, Alabama Gov. Kay Ivey, a Republican, signed into law a controversial abortion bill that will make performing an abortion at any stage of pregnancy a felony punishable by 10 to 99 years or life in prison.
The bill contains an exception for when the pregnancy creates a serious health risk for the woman, but not an exception for rape or incest. Only those who perform the abortion, not the woman receiving it, would be punished.
Kentucky, Mississippi, Ohio and Georgia have approved bans on abortion once a fetal heartbeat is detected, which can happen in the sixth week of pregnancy.
The Associated Press contributed to this report.