Soriano was examined by team physician Christopher Ahmad at New York-Presbyterian Hospital, where an MRI revealed similar results to another examination made last Wednesday in New York.
The Yankees have no definite timetable for his return.
"My hope is it's just the 15 days, but I can't tell you if that's what it's going to be," Yankees manager Joe Girardi said.
Soriano last pitched on Friday against the Red Sox, but he has been complaining of soreness since appearing in consecutive games on April 30 and May 1 against the Blue Jays at Yankee Stadium.
He attempted to throw a bullpen session on Monday at Tropicana Field, but Girardi told Soriano to stop because he felt stiffness in his pitching elbow.
Girardi also may speak to Soriano about his postgame comments on Monday, which raised eyebrows. He said that the Yankees' relievers should not be blamed for the team's current six-game losing streak.
"To me, I don't think the bullpen [is] the problem right now," Soriano said. "I think it [is] the hitters. [Those] things happen sometimes."
Soriano also said that his absence did not seem to have affected the team's fortunes.
"In these situations, how the team lost, that would not be the situation when I'm supposed to be in the game -- the eighth," Soriano said. "Everybody sees we've been losing by two, three runs. I don't think it would be the situation that I'd be in the game."
Girardi paused when asked about Soriano's comments.
"My thought is, we win as a team and we lose as a team," Girardi said. "Everyone on this club can always do a little bit more, and that's the bottom line. So you can take that for what it's worth.
"... What I do with my players, we try to keep it in-house, and that's what I'll do."
In the first year of a three-year, $35 million deal to serve as Mariano Rivera's setup man, Soriano is 1-1 with a 5.40 ERA in 16 appearances.
He has been uncharacteristically wild with the Yankees: Soriano has walked 11 batters (one intentionally) in 15 innings after issuing just 14 free passes in 62 1/3 innings last year as the Rays closer.
"He's thrown the ball really well for us at times and struggled at times," Girardi said. "Unfortunately, he hasn't felt good lately. We just need to get him back, get him healthy."
In a corresponding roster move, the Yankees recalled outfielder Chris Dickerson from Triple-A Scranton/Wilkes-Barre. New York had been carrying 13 pitchers because Soriano was burning a roster spot.