"I think it's improved each day. But we're being very cautious with this.
"There's no reason for him to completely blow it out, because it's an injury that if he hurts himself and really pulls it, we could lose him for a long time. So, we'll be cautious with him, shut him down and get him right. Hopefully, he'll only miss a couple of starts, and [we'll] go from there."
Lee is 0-1 with a 1.96 ERA thus far in 2012. He threw 10 shutout innings against the Giants on Wednesday. His move to the disabled list is retroactive to April 19, so the earliest he would be eligible to be activated is May 4 against the Nationals.
"Obliques, you just don't know how long they'll take, but he's shown improvement," Amaro said. "We're hopeful that he's only going to miss a couple starts. We have an off day in between [on Thursday]."
Amaro said the injury didn't occur because Lee pitched 10 innings. Lee was the first Major-League pitcher to throw 10 shutout innings since Mark Mulder of the Cardinals did it on April 23, 2005.
"I think it just happened," Amaro said. "He went through that game pretty well, pretty efficiently. He didn't show any signs of fatigue or anything like that. He was crisp in the 10th."
In his career, Lee has been on the disabled list in 2003 for a strained lower abdominal muscle/hernia, when he was with the Indians, in 2007 for a right abdominal strain when he was with the Indians, and in 2010 for a right lower abdominal strain when he was with the Mariners. Amaro said he doesn't think the current injury is similar to Lee's previous injuries.
Right-hander Kyle Kendrick will start in place of Lee on Monday against the Diamondbacks in Phoenix. Kendrick has posted a 1.93 ERA in four games this season.
The Phillies have recalled left-hander Joe Savery from Triple-A Lehigh Valley. Savery is expected to join the Phillies by gametime on Sunday against the Padres. Savery has a 3.86 ERA in 2 1/3 innings this season with the Phillies, and a 0.00 ERA in 2 2/3 innings at Triple-A.
Sarah Trotto is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.