Sheikh Mohammed bin Rashid, Vice President and Ruler of Dubai, sent similar messages of support to Mr Zelenskyy and Prime Minister Denys Shmyhal.
Wednesday will mark 31 years since Ukraine gained independence from the former Soviet Union.
The landmark event is typically celebrated fervently in the country, but the day will be a much more muted affair against the backdrop of war.
Independence Day is usually marked with a large military parade in the capital Kiev but no celebrations will be held this year amid tightened security measures.
The UAE has offered crucial assistance to Ukraine and thousands of its people displaced by the conflict.
In June, the UAE sent a plane carrying 52 tonnes of food for Ukrainian refugees in Bulgaria.
It is estimated that Bulgaria is hosting more than 90,000 people who fled Ukraine.
In the same month, the Emirates dispatched more than 27 tonnes of food and medical supplies to support Ukrainian refugees in Poland.
Before that, the Emirates sent six planes to Poland and Moldova, carrying more than 156 tonnes of food and medical supplies.
In March, the UAE announced it would provide relief aid to affected civilians in Ukraine worth $5 million in response to an urgent appeal by the UN.