The Arizona law would have prevented women from receiving a medication abortion between their seventh and ninth week of pregnancy.
Immigration activist groups have filed a complaint against the US Customs and Border Protection agents.
Arizona Governor Jan Brewer signed a bill into law last week allowing state health authorities to conduct surprise inspections of abortion clinics without a warrant.
In a victory for Arizona women, the US Court of Appeals for the Ninth Circuit has blocked the state's restrictions on medication abortion.
"With today's disappointing ruling, Arizona women's constitutional rights and access to safe, high-quality reproductive health care have been diminished, simply by virtue of where they live."
A wave of new anti-choice laws is currently making its way through the legislatures of several states, including Arizona, Oklahoma, South Dakota, West Virginia, Georgia, and Alabama.
The bill was strongly opposed by LGBT groups who have seen businesses in other states - such as florists, photographers, and bakers - refuse to provide services to same-sex couples. Members of the Arizona business community also opposed the bill, as did politicians on both sides.
The Supreme Court decided today to reject a case that would have been a direct assault on Roe v. Wade.
Arizona joined Kansas last week to create separate voter registration systems for state and local elections. The creation of two separate voter registration systems could translate into thousands of disenfranchised voters.
President Obama announced last Thursday his nomination of Diane J. Humetewa to the U.S. District Court of Arizona.
An Arizona bill intended to strip Medicaid funding from doctors and clinics that provide abortions was defeated in court last week.