The storm dropped rain and quarter-sized hail in the area. In some of the worst hit areas, about six feet of standing water were reported after more than an inch and a half of rain fell in about an hour.
Parts of the BYU-Idaho campus were also flooded, prompting the school to shut down for the rest of the day.
The school says classes will resume Wednesday except for any that are scheduled to be in the Smith Building.
The school also says that reports circulating about a collapse at the BYU-Idaho Center are false.
The Madison County Sheriff's Office says no injuries have been reported.