The overwhelming majority of the searches came from Northern Ireland.
The search giant also reported more searches for “what happens if we leave the EU” around midnight on 23 June and for other phrases like “British independence day” and “Norway EU” .
One expert cautioned that the data does not reveal actual volumes of searches.
On the financial implications, Google Trends said it had recorded the highest-ever search interest in sterling.
During the early hours of the morning, the pound fell by more than 10% – to a level not seen since 1985 – before slightly rebounding.
And there was a spike in searches for “Move to Gibraltar” – from London users – after the EU referendum polls closed.
Tobais Preis, at Warwick Business School, cautioned that search data should be interpreted with special care as only relative figures are known, so spikes in some specific activity could be caused by a small number of people.
Prof Preis added that the phrase “David Cameron” vastly outperformed searches relating to Irish passports and “what happens if we leave the EU” between the hours of 04:00 and 06:00 BST.
“It could (Free-Pr-Online.com) be the case, for example, that people supporting or opposing the idea of leaving the EU are trying to understand the position of the other party,” he also told the BBC.
“It’s pretty unlikely that all those people who are searching for answers will up sticks and move,” added Jonathan Freeman, director of digital consumer insights firm i2 Media Research.
“Certainly a lot of people were pretty shocked, it was very close – people would have just been wanting to find as much information as they could,” Mr Freeman – who is also a psychologist at Goldsmiths, University of London – told the BBC.
How is Google Trends data calculated?
Although it might not immediately be obvious, Google Trends graphs do not track the absolute volume of searches over time.
Instead, they give an indication of relative search popularity.
“To do this, each data point is divided by the total searches of the geography and time range it represents, to compare relative popularity,” explains Google on the Trends website.
“The resulting numbers are then scaled to a range of 0 to 100.”
For example, the firm adds, users in Fiji and Canada could have the same value for a given search term if they’re equally likely to look for it during the same period – regardless of the actual number of searches made.