Dr. James Andrews, after seeing Soriano on Wednesday, prescribed rest for two more weeks and then a conservative throwing program.
Making the announcement, Yankees general manager Brian Cashman said the ligament is the same one on which Soriano had Tommy John surgery back in 2004, and exploratory surgery in 2008.
"We are going to get him back as soon as practical, not as soon as possible, but as soon as practical because when he is right you know what he can do," Cashman said.
Soriano has been out since May 14 with what the Yankees described as elbow inflammation. The 31-year-old Soriano, who was signed to a three-year, $35 million contract this offseason, is 1-1 with a 5.40 ERA. In his place, Joba Chamberlain has been the main eighth-inning man, while David Robertson has worked the seventh.
"We have the personnel here and below [in the minors] to get us through," Cashman said.
Of the eight times in Soriano's career that he has been on the DL, six of them have been because of his right elbow.
"He obviously has a real issue," Cashman said. "It is something we need to take care of. We have to be careful with it. But if it is taken care of properly, it will be behind him, we hope, and we will move forward."
The Yankees claimed reliever Kanekoa Texeira off waivers and optioned him to Triple-A to add depth to their bullpen. They also transferred Phil Hughes to the 60-day DL to make room on their 40-man roster.
Soriano continues an odd start to his Yankees career. At his introductory news conference, Cashman openly said he disagreed with the decision to sign him because the GM didn't think it was right to allocate that many dollars to the team's setup man to Mariano Rivera.
Upon his arrival in spring training, Cashman and Soriano cleared the air. Soriano started the season strong and Yankees fans were abuzz about a bullpen trio of Chamberlain to Soriano to Rivera. The combination was quickly labeled Jo-So-Mo.
The buzz faded when Soriano struggled, blew off reporters and then, last week, said he hasn't been missed because the team was struggling because of the "hitters."
Before the elbow injury, Soriano missed time in Baltimore a month ago due to a back issue. Now, it is his elbow and the Yankees are hoping he will return before the All-Star Break.
"He is not healthy right now and we have to get him to that point," Cashman said.
Andrew Marchand covers the Yankees for ESPNNewYork.com. Information from The Associated Press was used in this report.