An "immediate and full joint investigation" will be conducted by the state's auditor general and the inspector general of the Department of Health and Human Services, Snyder said in a statement.
"The public health issues the people of Flint and Genesee County are facing warranted an internal review of how the state handled these situations," Snyder said. "I want some answers."
The department said it would fully cooperate with investigators and added it was "committed to promoting public health across the state."
Snyder himself has come under fire his handling of a water crisis that started when the state decided to save money
by switching Flint's water supply from Lake Huron to the polluted Flint River. Soon after the switch, the water started to look, smell and taste funny. Residents said it often looked dirty.
Last August, researchers from Virginia Tech discovered elevated levels of lead in the drinking water.
Doctors at Flint's Hurley Medical Center soon learned that blood lead levels in toddlers doubled and even tripled in some cases.
The elevated lead levels in children coincided with an increase in cases of Legionnaires' disease in Genesee County in 2014 and 2015.
Flint residents began getting gravely ill and in some cases dying in summer 2014
in one of the worst outbreaks of Legionnaires' in U.S. history. A county health director told CNN last month that attempts to find the source were hampered when the state wouldn't request federal assistance.
Genesee County Health director Jim Henry said he believes deaths could have been prevented, but he said the health department could not get help from the state of Michigan or the Centers for Disease Control and Prevention to determine the source of the illnesses.
Eventually, 87 people got Legionnaires' and nine died.
Henry, who was a supervisor at the time of the outbreak, said state officials purposely kept the CDC away when the county wanted to look at the highly corrosive Flint River as the Legionnaire's' uptick began.
"We were suspecting the city of Flint water supply," Henry told CNN. "That was the big red flag. Stickin' out like a sore thumb. We needed to check the water in that system."
Frustrated by what they see as a failure to reach an immediate solution to the crises, residents and their attorneys are increasingly turning to the courts.
More than a dozen lawsuits, including several class-action suits, have been filed in state, county and federal courts in Michigan. The range of remedies sought include monetary compensation for lead poisoning and refunds for water bills. Many of the suits name the city of Flint, the state of Michigan, Snyder and other local and state officials as defendants.