Tickets were made available for the public to apply for free of charge since January.
Officials allocated the parish 43,000 tickets for the public Mass in Abu Dhabi next week despite about 7,000 more local worshippers indicating that they wanted to attend.
Mathew Thomas, vice president of St Mary's parish council told Middle East website The National: "We have people here this evening from communities all over the world and it has been a hectic day.
"Because we only have 43,000 tickets for the 50,000 people who registered, we had to allocate them on a first come, first served basis."
Pope Francis is set to arrive in the UAE for the first time on Sunday.
He will celebrate a public Mass at Zayed Sports City in the capital Abu Dhabi on Tuesday morning.
Thomas added that he was overjoyed by the huge response to the pontiff's visit.
"There has been a huge response and it's been really encouraging to see," he said.
"The biggest representation has been from the Filipino and Indian communities."
St Mary's parish has announced it will be running a bus service to the Mass from Dubai on the night before.
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