It happened in Ypsilanti Township, about 40 miles west of Detroit, around 2:30 a.m. with the couple's two young children in the home at the time, according to news reports.
Investigators told WXYZ-TV that the homeowners were on edge after an attempted home invasion earlier in the day.
"So, he's a little bit on edge, goes to sleep, thinks his wife is next to him. When he wakes up again, sees what he thinks is someone who is in his home, grabs his weapon and pulls the trigger," Derrick Jackson, with the Washtenaw County Sheriff's Office, told the news station.
Jackson said a 4-year-old child in the home first talked to 911, telling the operator their mother couldn't breathe, and then the husband told authorities he shot his wife in the chest. The 31-year-old woman died from the gunshot wound, WXYZ reported.
The husband was initially arrested but was released Friday afternoon.
Investigators said they believe the shooting was a tragic accident and no charges have been filed in the case.