"Eleven people who were in close contact with her were given preventive treatment last night and confined to their hotel rooms for 24 hours," said Christian Leyrit, the state representative in the northern Normandy region.
The 54-year-old woman, who arrived in France Monday, was placed under observation in a hospital in the city of Caen for six or seven days, he said, adding that the D-Day commemorations will not be affected by the incident.
The case is the 24th confirmed case of the A(H1N1) virus in France.
Obama will visit the German city of Dresden and the former Nazi death camp at Buchenwald next week before taking in D-Day commemorations in France.
French President Nicolas Sarkozy has said he and Obama would together visit the American war cemetery in Colleville-sur-Mer above Omaha beach on June 6.
Omaha was one of the main landing points for US troops in the Allied invasion of Nazi-occupied France on June 6, 1944, and the cemetery overlooking the beach is the final resting place for thousands of American troops killed in the dangerous operation.