Though there were news reports that suggested Ortiz took the selfie for promotional reasons due to a relationship he has with Samsung, he staunchly denied that had anything to do with the photo or that it was prearranged.
"It was a once in a lifetime moment," said Ortiz. "How did I know he would let me take a picture with him?"
When did Ortiz decide he could actually take the selfie?
"It was right at the moment when I gave him the jersey and he asked to take a picture now or whatever, so I said, 'Oh, wait a minute. Let's see if I can get away with one.' I was lucky that I did," said Ortiz. "I think it was something I'm never going to forget. People went crazy about that."
By Wednesday evening, Ortiz's selfie had generated nearly 40,000 retweets.
"You don't get to see that every day," Ortiz said. "It wasn't anything promotional or anything like that. Who knows that you're going to be able to take a picture with the president or a selfie? How many people can guarantee that?"
If any other player besides Ortiz had snapped the selfie, the Red Sox might have been surprised. But in this case?
"Let's not be surprised about what David Ortiz does, ever," said left fielder Jonny Gomes. "That was pretty cool, and I think it was pretty cool that Obama was on board with it, too."
Ian Browne is a reporter for MLB.com. Read his blog, Brownie Points, and follow him on Twitter @IanMBrowne. This story was not subject to the approval of Major League Baseball or its clubs.