In making the ruling, U.S. District Court Judge Lee Yeakel wrote that forcing the clinics to meet the same standards as hospital-level surgical centers "imposes an undue burden on the right of women throughout Texas to seek a previability abortion."
That part of the Texas law was scheduled to take effect on Monday; critics of the law say it would have required the closing of a majority of 19 abortion clinics.
The Texas Department of State Health Services and the Texas Medical Board filed a notice of appeal.
The controversial law, which was signed by Gov. Rick Perry last year, is considered one of the most restrictive in the country.
The Center for Reproductive Rights brought the lawsuit on behalf of some of the clinics, and it called the federal judge's ruling a victory.
"The court has made clear that women's well-being is not advanced by laws attacking access to essential health care, and that rights protected by the U.S. Constitution may not be denied through laws that make them impossible to exercise," said Nancy Northrup, president and chief executive officer of the Center for Reproductive Rights.
"Texas women still face serious threats to their rights, health, and ability to obtain safe, high-quality reproductive health care from reputable doctors in their communities. But at least for the moment, today's victory is vital in preventing politicians' scorched-earth assaults on women's health care from causing even more harm than they already have."
The state law also banned abortions past 20 weeks of gestation, tightened usage guidelines for the drug RU486, and it requires doctors who perform abortions to have admitting privileges at a hospital within 30 miles of the clinic at which they're providing such services.
Last year, Yeakel overturned the requirement that doctors have admitting privileges, but a federal appeals court reversed the decision.
The 20-week ban provision took effect last year, while enforcement of the remainder of the law is slated to take effect in September.