The No. 4 golfer in the world even had his wife change his password.
McIlroy was turned off about the social media platform following a slight from Elkington, a former PGA champion.
On June 16, Elkington wrote: "Rory is so bored playing golf...without Tiger the threshold is prolly 4 majors with 100mill in bank."
McIllroy bit back by saying: "More like 200mil...not bad for a 'borded' 28-year-old...plenty more where that came from." He included a screenshot from his Wikipedia page with his list of career wins.
"New you were a money guy. Jack [Nicklaus] won 18 and never mentioned his total cash," Elkington responded.
"That's why jack designed 100's of golf courses...and it's knew...mustn't have taught grammar in the 50's," McIlroy replied.
McIlroy married wife Erica Stoll in April at a castle in Ireland. She helped him curb his Twitter distraction.
The defending Irish Open champion told reporters about the journey off of the social media platform on Wednesday.
"I must have wrote that tweet and deleted it about five times before I actually sent it," McIlroy told reporters, according to CNN.
"I sort of regret sending it at the end but I actually gave my wife, Erica, my phone and my Twitter and told her, 'Change my password to something else and don't tell me what it is.'"
"So as of the time being, I'm off social media just because of that reason. I don't need to read it. It's stuff that shouldn't get to you and sometimes it does."
"It is not what was said," McIlroy told reporters. "It was who said it and anyone who has been in that environment should realize how hard golf is at times. That is the thing that got to me more than anything else."
"If it was written by a member of the media or something I could let it slide, because I can sort of say to myself, they don't really know how it is and they don't know what you have to deal with."
"But a former player that has won a major and been successful, that's sort of why it got to me and that's why I sort of retaliated a little bit."
Elkington's comments came after McIlroy missed the U.S. Open cut by four strokes.
McIllroy won the 2014 PGA Championship for his last major title. The 2017 British Open begins on July 20 at Royal Birkdale in Southport, England.
He won the 2016 Tour Championship and FedExCup in September at East Lake.