Beckett and manager Terry Francona both said that the injury could have been caused by the pitcher sleeping on his arm.
"I think sleeping is definitely part of it," Beckett said. "I sleep like most 28-year-old guys. The only thing is, I have a different stress load on my body. It ends up costing me time on my job."
However, Beckett added that the issue was not isolated to just Sunday, and that he's dealt with it on and off this season. But he said that this is the first time it got to the point where taking some time off was necessary.
"Yeah, it's just something I've been dealing with," said Beckett. "At some point and time, [we] just have to figure out what the [heck] it is. Obviously, it's not what I want, but at this juncture, it's something that needs to happen. Obviously, there's something going on."
Beckett, asked if he would undergo tests to make sure there is no aneurysm or anything else of that magnitude, said he has been given assurances that there are no such issues, and that those type of tests probably won't be necessary.
"I haven't," said Beckett. "I'm not a big fan of those arthograms. I think they cause a lot of unneeded soreness. I think, if it gets to that point, we'll do whatever we need to do. I don't think that's what it is. Any time something is wrong with your arm and you're a baseball player, or especially a pitcher, you think the worst first. I've been kind of reassured by people that it's not that."
Still, he wants to get the problem under control.
"It feels all right," Beckett said. "I just have some numbness in fingers that obviously I'm not used to having. As far as pain goes, there's not very much pain at all with it. It's just, like I said, you have to figure out what it is or it gets so bad to where it gets to be a really bad problem.
"It's something that we've dealt with. Like I said, I've never had to deal with it on that level. It's something we've monitored over time. It hasn't ever festered [like this] until now."
With off-days on both Thursday and Monday, the Red Sox were easily able to rearrange the rotation. Paul Byrd, Jon Lester and Daisuke Matsuzaka will start the weekend series in Toronto.
Beckett, assuming the numbness goes away, will open the three-game showdown at Yankee Stadium, followed most likely by Byrd and Lester.
Is Beckett confident he'll pitch Tuesday?
"I don't know," Beckett said. "It's still seven days away, so we'll see."
After a breakout season last year, Beckett has struggled a bit with his consistency this year, going 11-9 with a 4.34 ERA over 23 starts.
"I haven't ever dealt like it on this level, on the day that I was pitching," Beckett said. "Some days were bad, some days were good. But I've never had to deal with it on this level on the day that I pitched."
Ian Browne is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.