The Irishman started strongly at the Killarney event but concluded the day's play on a 1-under 70.
McIlroy's performance caused Townsend to tweet: "McIlroy's course management was shocking.
"[It was] some of the worst I have ever seen beyond under-10 boys' golf competition."
Angered by the comments, the 22-year-old tweeted in reply: "Shut up... you're a commentator and a failed golfer, your opinion means nothing!"
The US Open winner went on to defend his caddie, JP Fitzgerald, who has been with the player since 2008.