The City Council voted unanimously on Tuesday to restrict staff from traveling to the state on city business.
The council also called on city officials to look into canceling contracts with businesses in the state.
The new Arizona law requires police enforcing another law to question people about their immigration status if there is reason to suspect they are in the country illegally.
Critics say it will lead to racial profiling of Hispanics.
But supporters say the law is needed because the federal government has failed to secure the border.