PHILADELPHIA -- Phillies general manager Ruben Amaro Jr. said Wednesday he's relieved by the MRI results on the elbow of Cliff Lee but said the club isn't ready to project how long the ace will be out or how that will affect his team's approach before the July trading deadline.

"We just don't know yet," Amaro told ESPN.com. "It could be two weeks. It could be three weeks. It could be four weeks. Who knows? It could be 30 weeks. We think it will be shorter. It's a pretty mild strain. ... We just have to be really cautious with him."

Lee was diagnosed with a Grade 1/Grade 2 strain of his left elbow Tuesday night after an MRI in Philadelphia earlier in the day. He had complained of soreness after throwing 6 2/3 innings and 116 pitches Sunday in a start against the Reds.

"He's pitched a lot, but his arm has never really been hurt," Amaro said. "He's had abdominal issues but never an arm [injury]. So he's perplexed. He doesn't like to be hurt. He actually fought us a little [about going on the disabled list] until he got the MRI and we told him the MRI results."

Phillies lefty Cliff Lee has a mild elbow strain and will rest for a week before he resumes throwing. Mitchell Leff/Getty Images

Lee, who will turn 36 in August, spent time on the disabled list in both 2007 and 2010 with abdominal strains and missed about three weeks in 2012 because of a strained oblique. But this is the first time in either his major league or minor league career that he's been placed on the DL with any type of arm issue.

He has pitched 1,401 2/3 innings since 2008, a workload surpassed by only four other active pitchers -- Justin Verlander (1,439), Felix Hernandez (1,426 1/3), CC Sabathia (1,415) and James Shields (1,411).

Lee's contract pays him $25 million this season and $25 million next season. He has a vesting option for $27.5 million in 2016, or a $12.5 million buyout. He also has a limited no-trade clause that allows him to block deals to 20 teams.

Lee's injury is a major blow to a team whose strength is its starting pitching, as the Phillies are trying to make what might be their final run at contending with an aging core group of players. Lee has been a subject of massive trade speculation, and figured to be a much-talked-about name in July if the Phillies fall out of the race. Amaro, however, isn't ready to discuss the implications of Lee's injury on the Phillies' midseason trade plans.

"I don't have any idea yet about that," the GM said. "Frankly, we really don't know what we have. ... There's a lot of parity and a lot of mediocrity out there -- including us. We're playing like a mediocre club. We're playing like a .500 ballclub."

The Phillies went into Wednesday's game in Miami two games under .500 (20-22) after winning three games in a row. But with Lee out for several weeks, Amaro admits they've "lost quite a bit of pitching depth" because of injuries to their most advanced minor league starters. Most recently was a shoulder injury suffered by Jonathan Pettibone, who has started 20 games in the big leagues over the past two seasons.

Amaro said right-hander David Buchanan, who impressed the Phillies in spring training, was "the most likely choice" to replace Lee in the rotation, but the GM wasn't willing to commit to a call-up of Buchanan yet.

"We're still trying to figure it out," Amaro said. "It may actually end up being a merry-go-round, with whoever pitches the best."

Amaro said Miguel Alfredo Gonzalez, the Phillies' much-ballyhooed free-agent signing from Cuba, is not yet a candidate to pitch in the major leagues. He has been on the disabled list since March and is still on a rehab option with Class A Clearwater. The Phillies' top pitching prospect, former No. 1 pick Jesse Biddle, is "not ready to pitch in the big leagues," Amaro said.

The Phillies called up first baseman/outfielder Darin Ruf to replace Lee on the roster. But that is likely to be only "a three-day fix," Amaro said. Ruf just came off the disabled list himself after straining his oblique muscle in spring training.