Valverde had approximately 20 cc of fluid drained from his right calf at the Methodist Hospital on Thursday by team physician Dr. David Lintner. There is still approximately 60 cc of fluid remaining that will have to be removed on Friday, at which time doctors will make a small incision in order to drain the remaining fluid.
Valverde is expected to miss up to three weeks after the final procedure on Friday.
The 30-year-old closer was placed on the 15-day DL with a strained right calf, retroactive to Monday (April 27) and is eligible to be reactivated on May 12.
Valverde is 0-1 with a 5.63 ERA and two saves in eight relief outings this season.
Alyson Footer is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.