Thompson issued an order temporarily blocking enforcement of the law.
Thompson's decision comes days after a federal appeals court blocked a similar law in Mississippi.
Planned Parenthood and others filed a lawsuit over the Alabama law last year.
Supporters of the law say it would make clinics safer. Clinic operators say the law would force the shutdown of all but two of Alabama's five clinics.
Thompson says the Alabama law would place an undue burden on women.
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