Rain fell across Al Ain overnight and into the early hours of Monday morning, the National Centre for Meteorology reported.
Forecasters expected the tropical storm to weaken by Monday evening.
A briefing by the UAE’s National Emergency, Crisis and Disaster Management Authority (Ncema) on Sunday set out the measures in place to mitigate the effects of the cyclone.
Police are patrolling coastlines, wadis and mountains, and residents have been told to avoid these areas, and all schools, universities and colleges that could be affected have moved temporarily to distance learning.
Abu Dhabi also announced that in Al Ain, government entities and companies will on Monday work remotely; Covid-19 testing and vaccination tents have been closed; private sector companies urged to use remote working; access to Jebel Hafeet closed; and residents urged to avoid leaving home except in an emergency.
Authorities are also primed to assist with evacuations if needed.
The Ministry of Foreign Affairs and International Co-operation has also been in touch with Emiratis in Oman and provided all necessary information regarding returning to the UAE.
Authorities have also ensured the safety of buses carrying staff to and from their places of work.
“The storm can reach wind speeds of between 120 and 140 kilometres per hour,” an NCM forecaster said.
Authorities will also monitor houses in potentially affected areas and help with evacuations if needed.
At least nine people died after storms lashed parts of Oman and Iran on Sunday.
Thousands were evacuated from coastal areas in Oman.
Shaheen was later downgraded to a tropical storm after it hit land, a local meteorology service said.
It had already brought torrential rain and high winds to Oman.
Forecasters say the cyclone would carry winds of up to 110kph as it approached Muscat.
Some schools in the northern and eastern parts of the country have been told to resume remote learning temporarily as a safety precaution.
All pupils in Al Ain, for instance, will study from home until Tuesday.
Expo 2020 Dubai officials say they are keeping a close eye on the weather.
Expo spokeswoman Sconaid McGeachin said the team would issue advisories to the public if heavy wind and rain struck the emirate.
Cyclone Shaheen is expected to weaken significantly after landfall. It is set to leave the UAE on Monday.
People have been urged to follow official news sources and not to spread rumours.