The force received 13,108 calls on its emergency number, 999, over the past 36 hours — an average of six a minute.
Most were either weather-related or accident calls. However, the force did not reveal how many accidents had been reported since Monday morning.
Dubai Police's command and control centre also received 1,959 non-emergency calls on its 901 number.
Brig Turki bin Fares, deputy director of the operations department at the force, urged motorists to keep a safe distance between cars and reduce their speed.
“Slow down as rains make roads slippery. Avoid speeding during unstable weather to avoid accidents,” he said.
Brig bin Fares also advised drivers to start a bit early and check their planned route to ensure roads are clear.
“People should follow safety instructions and regulations to avoid any accidents,” he said.
Dubai Police said they had taken steps to deal with any incidents, especially in the mountains, low-lying areas that are prone to floods and desert areas that are frequented by people during the cooler months.
The rainy start to the week in the UAE will continue through Tuesday and into Wednesday, according to a National Centre of Meteorology forecast.
Rain hammered parts of the country on Monday, with motorists urged to exercise caution on the roads to avoid accidents.
Residents can expect cooler temperatures of about 23ºC on Tuesday after the rain stopped around 1pm.
Lighter showers are expected on Wednesday, with highs of about 25ºC along the coast, before conditions dry up on Thursday.