Rosa Dejesus Perez-Siguencia, 35, and Angel Rigoberto Garcia-Tapia, 34, were held without bail at the request of federal immigration officials, jail records indicated.
They admitted to police they left their baby boy in the car while they went to a pharmacy, the (Minneapolis) Star Tribune reported.
A passerby heard the infant crying inside the car and called police. Officers pulled the red-faced, sweating infant from his baby seat, located the parents in the drugstore and arrested them, police said.
Even though the car's windows were rolled down about 6 inches, the air inside the car was recorded at 111 degrees Fahrenheit, police said.
The outside temperature was nearly 86 degrees at the time and felt like 89 degrees due to the humidity.
The infant "appeared to be in great distress," the criminal complaint against the parents stated.
The baby was taken to a hospital and appeared to have recovered fully, police said.
Police Lt. Greg Reinhardt was quoted by the newspaper as saying the couple appeared "remorseful."