"Chavez is the solution and Jayson Nix is the solution, and whoever we have in the farm system are going to have to be the solution," Cashman said. "I'm very comfortable with Eric Chavez as Alex's replacement."
Chavez, a 15-year veteran with six Gold Gloves earned as the third baseman for the Oakland Athletics, becomes the Yankees' starting third baseman and Nix, a utility player who has filled in at five positions this season, will serve as his backup.
The Yankees also recalled utility infielder Ramiro Pena from Triple-A Scranton/Wilkes-Barre to shore up their bench in Rodriguez's absence.
Cashman said Eduardo Nunez playing third base is "not on radar at moment," but he didn't rule it out.
The Yankees demoted Nunez to the minors in May after he committed four errors in 20 games. Nunez just returned to shortstop at Triple-A after missing two months with a thumb injury.
Rodriguez suffered a nondisplaced fracture of the fifth metacarpal, the bone that connects the little finger to the wrist, when he was struck on the left hand by an 88 mph changeup in the eighth inning of Tuesday's 4-2 loss to the Mariners. The injury is not expected to need surgery, and the Yankees believe Rodriguez will be sidelined between six and eight weeks.
Because of that, Cashman said he will not actively pursue a third baseman from another organization.
"Because we're going to get him back, I don't see this as a particular area of need," Cashman said. "It doesn't mean I won't listen."
Among the third basemen expected to be available at the trade deadline are Chase Headley of the San Diego Padres, Placido Polanco and Ty Wigginton of the Philadelphia Phillies and Chone Figgins of the Mariners.
"I'm not about to gut my farm system for any of those guys," Cashman said.
Cashman didn't seem to think he could swing the kind of deal he did on Monday, acquiring Ichiro Suzuki for two midlevel pitching prospects.
"Lightning doesn't normally strike twice," Cashman said.
Chavez is batting .269 with eight home runs and 20 RBIs in 64 games this season, only 28 of which have been at third base.
Chavez's injury history makes him a risk as an everyday player, but Cashman is confident in the veteran's durability.
"That's his job, to fill in as needed," he said. "That's what he's here for. I expect him to be able to play third base for us every day, and to play it well."