The amendment goes to the state House of Representatives, The (Nashville) Tennessean reported Tuesday. If it passes there, it will be on the state ballot in 2014.
The measure aims at reversing a state Supreme Court ruling in 2000. It declares explicitly that the Tennessee Constitution does not protect the right to abortion.
All 20 Republicans and four Democrats in the Senate supported the amendment, which passed 24-8 late Monday.
"This resolution is only about letting the people decide whether they want their elected representatives to make the laws on abortion," said state Sen. Mae Beavers, a Republican who sponsored the amendment.
Supporters say the amendment would allow the legislature to approve laws restricting abortion.