The team did not reveal the results of the visit.
"Until that [second] consultation takes place, no further information will be provided," the Yankees said in a statement.
Eovaldi made quick work of the Red Sox in the bottom of the first inning, using just 12 pitches to retire the side in order. But Eovaldi would not return to action the following inning.
Both manager Joe Girardi and pitching coach Larry Rothschild were concerned following the first inning upon noticing that Eovaldi's velocity was not as high as usual.
Girardi and Rothschild grilled Eovaldi, and it took some time to get the truth out of him, but they knew better than to push Eovaldi further when he revealed the injury.
"Larry asked him three or four times, 'Are you OK?,'" said Girardi. "He kept saying, 'Yep. Yep. Yep.' Larry asked him again. He finally said he felt something in his elbow. We took him out."
It was the shortest outing of the year for Eovaldi, who missed the end of last season due to inflammation in his right elbow. The right-hander underwent Tommy John surgery in 2008, shortly before he was drafted.
Girardi was forced to go to his bullpen early and often on the night, using seven relievers deftly while the offense swung the game in the Yankees' favor.
"That was the reason that we went to the eight-man bullpen," Girardi said. "That's always a concern when you don't have a true long [reliever] down there, you don't have someone that can give you 100 pitches. The guys did an incredible job. We mixed and matched, and they all did their job and got big outs when they had to."
Aaron Leibowitz is a contributor to MLB.com based in Boston and covered the Yankees on Thursday. This story was not subject to the approval of Major League Baseball or its clubs.