He is expected to miss four to six weeks.
Rodriguez met with Dr. Lee Kaplan in Miami on Sunday, and Kaplan recommended that Rodriguez go under the knife. The surgery will be performed by Dr. Kaplan at the University of Miami on Monday.
An MRI on Friday first revealed the tear.
Yankees manager Joe Girardi said on Sunday that, if Rodriguez opted for surgery, undergoing the procedure now would be ideal given the Yankees will have four days off during the All-Star break.
"There's no doubt we're going to miss him, but we need to find a way. As I've said several times already this year, some people are going to have to step up," Girardi said. "Up to this point, this team has. We certainly look forward to getting a healthy Alex back into our lineup, because we know what he adds to this team."
If he hadn't opted for surgery, Rodriguez could have tried to play through it and have the procedure in the offseason.
But Girardi expressed concern that Rodriguez would be forced to play eight consecutive games on turf after the All-Star break if he decided to forgo surgery. The Yankees open the second half with a four-game series in Toronto and then head to Tampa Bay for a four-game set.
Rodriguez originally suffered the injury on June 19 in Chicago. He thought about scoring on a passed ball, but ultimately decided against it. And in the process of turning back toward third base, Rodriguez tweaked his knee.
"It's hard to get into missing 20, 30, 40 games when you don't know, but at the same time you don't want to limp toward the finish line," Rodriguez said after not playing in the Yankees' 5-4 win over the Rays on Saturday afternoon at Yankee Stadium. "The most important games are played at the end."
He had already withdrawn from the 2011 All-Star Game on Tuesday in Phoenix.
"It is what it is," Rodriguez said. "Most players play with bumps and bruises, but you never expect it to be a tear. Obviously, it was disappointing."
CC Sabathia played through the same injury last season. He said he spoke to Rodriguez recently about it. And while he didn't advise Rodriguez to have surgery, he seemed in favor of the move.
"I think it's good," Sabathia said after getting his 13th win in a complete-game shutout on Sunday. "... We definitely want him in the lineup but we want him to be right."
Outfielder Andruw Jones also suffered from the injury during 2008, when he played for the Dodgers. He woke up one day and said he couldn't walk and opted to have the surgery. The injury caused a leaking of fluid in his knee and a cyst on the back of his knee had to be drained.
As he tried to come back, Jones said he was running in his second week and came back in four weeks, but that was too soon and he got hurt again and landed back on the disabled list. Jones added that it affected his power and he did not have his leg under him at the plate.
Rodriguez has not hit a home run in his past 85 at-bats, the longest single-season drought of his career, and has just seven extra-base hits in that stretch.
Rodriguez, who is batting .295 with 52 RBIs in 80 games, has just 13 home runs so far, putting him on pace for 24 for the season. That would snap his streak of 13 straight seasons with 30 or more home runs.
"I just don't think that he has the drive in his backside that he needs to have to be the power hitter that he's capable of being," Girardi said Saturday. "I still think he can be productive and get his base hits but I don't think you're going to necessarily see him drive the ball as much."
Girardi said he had watched Rodriguez in the past few games, including an 0-for-4 night against the Rays on Thursday, and when he decided to take him out of Friday's lineup, he broached the topic of Rodriguez having an MRI.
Eduardo Nunez is likely to step in at third base. Nunez is hitting .278 with three home runs and 14 RBIs this season.
"If you don't have Alex for a while, you tell Nunie, don't try to be Alex, just be Nunie. But it's not someone that you can really replace," Girardi said.
Ian Begley and Mike Mazzeo are regular contributors to ESPNNewYork.com.