The restriction - which was set to go in effect today - was among a host of new rules which critics say would have forced all but five of the sprawling state's 42 clinics to close.
Abortion is a key hot-button issue in US politics. Opponents have in recent years imposed a host of restrictions aimed at deterring women from ending their pregnancies and making it harder for clinics to operate.
The Supreme Court has upheld its 1973 landmark Roe v Wade decision legalizing abortion but has approved of a number of restrictions such as waiting periods and a ban on late-term abortions.
The bill bans all abortions after 20 weeks of pregnancy, limits the use of the abortion pill RU486, imposes expensive new building codes on clinics, and requires abortion providers to get admitting privileges at a nearby hospital.
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Federal judge Lee Yeakel ruled that the admitting privilege requirement "does not bear a rational relationship to the legitimate right of the State in preserving and promoting fetal life or a woman's health and, in any event, places a substantial obstacle in the path of a woman seeking an abortion of a nonviable fetus and is thus an undue burden to her."
Many hospitals ban their physicians from performing abortions and will not grant providers admission privileges because their low-risk practices do not result in a high enough volume of admissions, Yeakel noted in a 26-page opinion.
Limits on the use of the abortion pill were upheld because the law includes a provision which accounts for threats to a woman's health or life, Yeakel ruled. The other restrictions were not addressed in the lawsuit.
Texas Governor Rick Perry vowed to "continue to fight" for the law.