"We have some work to do but we think we have the right person in custody," Chicago Police Supt. Garry McCarthy said.
Sutton was gunned down in alleged gang crossfire Wednesday night while she sat in her front yard selling candy to neighborhood residents.
McCarthy said he expects charges to be filed against the suspect soon.
"Bringing heaven's shooter to justice will not bring her back"," Chicago Mayor Rahm Emanuel said in a statement. "But I hope it will provide some level of solace to her family.
"I will continue to fight to make sure the Chicago police has the resources it needs to stop the violence."