The Bantams saw off Premier League opposition in the form of Wigan on Tuesday to book their place in the last eight, and the visit of Arsene Wenger's team will be the first time the Coral Windows Stadium has played host to a top-flight club since 2001.
"I think everyone at the club will be pleased and excited by this draw," Parkinson told City's official website. "We were all waiting and hoping for a big draw to come out and we've certainly got that with the visit of Arsenal.
"It's a great draw for the city of Bradford, not just the club itself, and it's a nice reward for all the hard work that our staff put in behind the scenes.
"To get one of the great teams of our country on home soil is going to be a great occasion for our supporters. We will give the game our best shot and try to make it as difficult as possible for them on the night.
"We will have a good chat about it (the Arsenal game) between the management and players tomorrow (Thursday), but after that we must concentrate on our other matches until the tie comes round. The game is going to be a massive occasion for the club but the league will always be our priority."