US District Court Judge Tanya Walton Pratt granted a preliminary injunction sought by Planned Parenthood of Indiana and Kentucky, which argued that the law was unconstitutional and violated women's privacy rights.
The law was set to take effect tomorrow.
Indiana and North Dakota are the only states with laws that ban abortions sought due to fetal genetic abnormalities, such as Down syndrome, or because of the race, sex or ancestry of a fetus.
The lawsuit filed by Planned Parenthood and the American Civil Liberties Union of Indiana also challenges the law's provision requiring that aborted fetuses be buried or cremated. Planned Parenthood currently disposes remains by incineration, as with other medical tissue.
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The measure was approved despite objections from many female legislators, including Republicans, who said it went too far.
The lawsuit was filed in April, and Pratt heard arguments from both sides on June 14. During that hearing, Indiana Solicitor General Thomas Fisher argued that Indiana's law was a response to DNA testing advances that permit fetuses to be screened for genetic defects or to determine their sex.
He said the state has an interest in "preventing discrimination" against fetuses based on such test results.
Pratt, who was nominated as a judge by President Barack Obama in 2010, in June 2011 blocked an Indiana law from taking effect that would have prohibited entities that perform abortions from obtaining state funding.
Her order became permanent in 2013 after the US Supreme Court refused to hear Indiana's appeal in the case.
Indiana had sought to prevent Medicaid enrollees from accessing health care at clinics operated by Planned Parenthood of Indiana and Kentucky because the organization provides abortions.