Mr Calderon has said the bill would damage relations between Mexico and the US border state
Mexico has urged its nationals to carry proper documentation with them to Arizona in response to a tough new immigration law in the US state.
In a travel alert, the foreign ministry says there will be a "negative political environment" for Mexican visitors and migrants.
The law, signed into law last week, requires Arizona police to question people on their immigration status.
The Mexican government has condemned the legislation as "discriminatory".
The law is due to come into effect in 90 days despite strong criticism from President Barack Obama and protests.
The alert recommends Mexicans travelling to Arizona to ensure they "act with prudence and respect local laws".
"As long as no clear criteria are defined for when, where and who the authorities will inspect, it must be assumed that every Mexican citizen may be harassed and questioned without further cause at any time," it reads.
It also reminds citizens that they are protected by international human rights laws.
Mexican President Felipe Calderon has warned that relations with Arizona would suffer and that his country would use all means at its disposal to defend its people.
Under the new rules, those unable to show that they are legally allowed in the US could be given six-month jail sentences and fined $2,500 (about £1,600).
The law was signed by Arizona Republican Governor Jan Brewer, who said it "protects every American citizen".
Supporters say not enough is being done at a national level to address the problem of immigrants and drugs crossing the border from Mexico to the US.
The state is home to an estimated 460,000 illegal immigrants.
Mr Calderon is due to discuss the issue with Mr Obama in Washington next month.