They added the force were "working tirelessly" and asked that the public avoid the area so as not to distract searchers.
They also thanked the public for respecting the privacy of the family.
A spokesperson for West Midlands Ambulance Service said they were called at 15:21 BST and found a teenage boy who had been pulled from the water on arrival.
"He was assessed but did not require further treatment and was discharged at the scene," the spokesperson said.
"Following several hours of further searching alongside police and fire colleagues, no other patients were found, and our resources were scaled back."
Draycote Water is a 240-hectare reservoir and country park, drawing its water from the River Leam, which then supplies drinking water to Rugby and Coventry.
Watersports such as sailing and windsurfing are popular at the site, and it also attracts anglers.
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