The victim was found dead in the 400-block of Valentine Way in Oswego on Tuesday at about 1:10 p.m., police said.
Oswego police were able to find the suspect after a witness reported seeing him running southbound across Wolfs Crossing Road. The suspect was taken into custody by police.
Police said a "caller reported that he believed his wife was in danger after observing, via home surveillance, a male subject run after his wife into their garage. The caller believed the male to be the wife's ex-husband."
When officers arrived they found an unresponsive woman who was later pronounced dead.
Police did not say how the woman died, and her age and identity have not yet been released.
OPD asked residents in the Prescott Mill, Hudson Pointe, and Echelon Oswego area to review surveillance footage related to the investigation.
Police also asked neighbors to look in their yards and garbage cans for any items that could be linked to the investigation.
The suspect in custody has also not been identified by police.