The Federal Emergency Management Agency (FEMA) is reporting two people are injured but there are no reports of casualties.
The US National Weather Service said the slow-moving category 4 storm delivered rainfall of up to 5cm per hour overnight.
The weather service said that Mawar could produce landslides, flash flooding and life-threatening storm surges.
"Treat these imminent extreme winds as if a tornado was approaching and move immediately to an interior room or shelter NOW!," the weather service in Guam warned on Wednesday evening.
