Abortion providers will be required to bury or cremate foetal remains in Texas from as early as September.
It comes as part of series of anti-abortion regulations that have been passed into law in the state.
It will also ban foetal tissue donation, and is said to be a response to unfounded claims that abortion clinics harvest foetal organs for profit.
This claim stemmed from discredited, unreliable videos according to the Texas Observer.
Another provision will implement possible felony charges for women who get second-trimester abortions.
Texas Alliance for Life spokesperson Joe Pojman said the bill is about "ensuring babies are treated in a humane manner - that their bodies are not desecrated, their organs are not harvested and sold".
State Representative Donna Howard said "politicians have no place in the medical exam room" and told supporters if they wanted to stop abortions then they should support contraception to prevent unwanted pregnancies.
Texas Observer reports that legal challenges by the Supreme Court are likely, given that in 2016 the courts struck down two provisions of Texas anti-abortion laws.
The court ruled that the state could not add restrictions that would "create a burden on access without evidence that the regulations are necessary for women's health".
Similar foetal remains measures in other states have previously been ruled unconstitutional.