Shamrock Rovers will play AC Milan in the second round of the Europa League qualifying at Tallaght Stadium.
The match will be played behind closed doors on Thursday 17 September
The Hoops beat Ilves on penalties to reach this stage.
They last played an Italian side when meeting Juventus a decade ago.
Zlatan Ibrahimovic is set to be part of the Milan squad as he is set to sign a new contract with the San Siro side.
AC Milan last played against an Irish side when they beat Athlone Town in 1975.
Seven-times European champions Milan have not won a major trophy since 2011, when they claimed the last of their 18 Serie A titles, and since then have frequently finished in mid-table.
They last played in the Champions League in 2013-14.
🇮🇹 | We have been drawn to play AC Milan at home in the @EuropaLeague 2nd Qualifying Round. #RoversInEurope pic.twitter.com/AUXEibNyhD— Shamrock Rovers FC ☘️ (@ShamrockRovers) August 31, 2020
"I think the football department would have preferred one of the two other teams we could have got on paper," club chairman Jonathan Roche told RTÉ Radio 1's News At One.
"They looked a bit more of an easier draw but it's great for our fans who go to our matches week in and week out, obviously before the Covid came in.
"It shows that this is real football. It's a real football club they play for. Our first-team players can come up against some great names like Zlatan etc on the Milan team.
"It's coming up ten years since we played Juventus in the Europa League in Tallaght, and we had a great night. Everyone at the club is really looking forward to it.
"It's great validation for our club, and all the other clubs in the league that do great work week in, week out."
In terms of the potential financial windfall, Roche admits it's not as great as it might have been had supporters been allowed into the game.
But he points out that the one-off nature of the tie might help the SSE Airtricity League leaders to cause an upset.
"Obviously it's behind closed doors, so we're going to miss out on that (revenue). And we're going to miss out on the experience of playing a two-legged match... going to the San Siro.
"But on the other side of things, it does level it out a little bit that it's a once-off match, even against the great Milan.
"It gives us some sort of chance. We're at home, we're in Tallaght.
"Dare to dream - funnier things have happened."
Dundalk have been handed the best possible draw as they will play unseeded Inter Escaldes of Andorra.
Inter Escaldes were the lowest ranked team. The Lilywhites will be away from home.
Coleraine's reward for shocking Maribor is a home tie with Motherwell, while Linfield will take on Floriana of Malta in Belfast.
Tottenham Hotspur have been drawn against Bulgarian side Lokomotiv Plovdiv.
Rangers will have to travel to Gibraltar to play against Lincoln Red Imps.
Europa League qualifying second round draw involving Irish teams:
- Shamrock Rovers v AC Milan
- Inter Escaldes v Dundalk
- Linfield v Floriana
- Coleraine v Motherwell