The House measure would ban insurance coverage for abortions and require women who wanted coverage to purchase a supplemental plan for an abortion, the latest effort by the most-populous Republican-controlled state to place restrictions on the procedure.
If enacted, the bill would take effect on Dec. 1 and make Texas the 11th state to restrict abortion coverage in private insurance plans written in the state.
The Republican-dominated Senate has passed a similar bill, and Republican Governor Greg Abbott has shown support for the measures.
The bill's backers say it would protect abortion opponents from subsidizing the procedure. A Democratic critic decried it as forcing people to buy "rape insurance."
"It's a question of economic freedom and freedom in general," Republican Representative John Smithee, the bill's sponsor, said in House debate on Tuesday ahead of the bill receiving preliminary approval.