The revelation comes weeks after an infant from the same part of the state was found to be infected with the virus.
Health investigators said there were direct links between the family of the three children and the family of the first infant found to have the virus. The families are not related by blood, health officials said.
None of the four children have symptoms of paralytic polio, health officials said, and none were vaccinated against the illness. Health officials said they were working with the Amish community to determine who may have been exposed to the virus.
Health Commissioner Dianne Mandernach, in a prepared statement, said the "general public is not at risk."
"These cases do not represent a generalized outbreak of polio virus infection," she said. "You are not at risk of infection unless you have had close contact with an infected person, and you have not been immunized against polio."
The first infant reported with the virus was the first reported case of polio nationally in five years. The baby had been diagnosed with immune system problems but didn't show symptoms of paralytic polio infection. The strain appeared to be related to the oral vaccine still used in some countries.
State and federal health officials were still investigating how the child became infected. Stool or spit from an infected person can transmit the virus.
Use of oral polio vaccine containing the live virus stopped in the United States in 2000, replaced with an injected vaccine made from the killed virus. The live-virus vaccine caused an annual average of eight cases of paralytic polio nationwide. The last naturally occurring case of polio in the United States was in 1979.
Minnesota's last case — related to the live-virus vaccine — occurred in 1992.
Health officials consider the disease eliminated in the Western Hemisphere. It persists in other parts of the world, with the vast majority of cases concentrated in India, Nigeria and Pakistan, according to the World Health Organization.
About 93 percent of Minnesota residents have had a full series of three polio shots, usually given during infancy.