More than an inch fell on much of the area and almost 4 inches were reported in Black Canyon City and New River, the National Weather Service said. Flash flood warnings were issued, with dry washes reported "with water levels at bankfull near many communities."
"We haven't seen a storm like this move through the Valley during the morning hours in quite some time," said April Warnecke, a meteorologist with KTVK-TV in Phoenix. "Any more rain that we do get is falling on already saturated ground."
Several thousand homes and businesses were reported to be without power.
More rain is expected in coming days. The Phoenix Fire Department offered free sand to residents trying to protect their homes but said recipients would need to supply their own bags and shovels.
The state Department of Transportation reported that several entrances and exits on Interstate 17, which connects Phoenix and Flagstaff, were closed. The highway itself was reported to be open.