The man, whose name was not released, was not expected to be charged or arraigned until at least Friday.
A suspected serial killer has been arrested in the deaths of five women in the city in just over a month - and he is also connected to an assault on a woman whose dog ran the attacker off, police said.
Local, state and federal investigators "have taken a collective sigh of relief," police Lt. Judy Horning said.
"The despicable individual responsible for this heinous rampage through our community has been captured," Mayor Virg Bernero said. "Our nightmare is over."
Police had been looking for clues and help from the public in five homicides since late July, including two this week, in the state capital, a city of 114,000 about 75 miles northwest of Detroit.
A 56-year-old woman was attacked Tuesday in her home, but her dog heard the commotion and charged the man, who fled. Her injuries were not life threatening.
Police credited her with providing key details that helped focus their investigation and led to a sketch of a suspect, but they declined to discuss the circumstances of the arrest or any motive.
Investigators had noted similarities between several of the slayings and a series of unsolved 2003 assaults. The 2003 victims were middle-aged or older women who lived alone, as were a number of the recent homicide victims.
Carol Wood, a Lansing City Council member, said her first reaction was one of "guarded relief" that police had identified a suspect in the death of her mother, Ruth Hallman, a 76-year-old community activist who was the first of the five women to be killed.
"I'm very hopeful," Wood said.
Hallman was found beaten in her home July 26 and died later. The other victims are Deborah Cooke, 36; Debra Renfors, 46; Sandra Eichorn, 64; and Karen Yates, 41.
Yates was found Wednesday afternoon by people who had come looking to buy a house. She died two days after Eichorn was found dead in the house she rented. Cooke's body was found Aug. 6 in a park, and Renfors was found dead Aug. 9 in a house.