The incident prompted anger among many politicians, some of whom saw it as a violation of Italian territory.
Rainbow for Africa said the incident happened on Friday evening when the French police brought a Nigerian migrant to the train station of the Italian border town of Bardonecchia.
The NGO said the police entered the clinic, which is in the train station, and demanded that the personnel conduct a urine test on the man because they suspected him of drug trafficking.
Massimiliano Fedriga of the right-wing League, which made big gains in the March 4 election, said the French had made Italy look like “the laughing stock of Europe”.
“French police do whatever they want on Italian territory without being disturbed as if they are at home. What happened in Bardonecchia is grave and shows how our so-called friends in Europe have little or no consideration for us,” he said in a statement.