Hill received a cortisone injection in the elbow and will begin a throwing program within 10 days. Hill is expected to rejoin the club on Friday in Pittsburgh.
"It's good news, but I have to be cautious," Hill said by phone.
Hill said he was thinking the worst when he arrived in Andrews' office. He was prepared to have elbow surgery Monday night or Tuesday.
"But I got the best possible scenario, but like I said before, I have to be cautious," Hill said.
Manager Manny Acta expressed relief that Hill's elbow injury was not serious.
"It's a big relief. I feel so good, not only for our ballclub, but for the kid, especially because I know he was very worried," Acta said.
The return of Fick: Acta said that Robert Fick will rejoin the Nationals on Tuesday. Fick has been on the bereavement list since his mother, Gloria, passed away because of lung cancer.
With Fick returning, the Nationals will make a roster move before Tuesday's game against the Braves.
Smoker visits Nats: Left-hander Josh Smoker, the Nationals' sandwich pick in the 2007 First-Year Player Draft, and his parents visited the team on Monday afternoon.
They had a meeting with Acta, amateur scouting director Dana Brown, broadcaster Don Sutton, team president Stan Kasten and catcher Brian Schneider. Smoker, a Georgia native, was told the team's plans for the future and how the club would like to have him in their plans.
Smoker is not close to signing a contract, but indicated that he wants to play for the Nationals. However, he has options, since he was accepted into Clemson University.
"We are still talking with them," Smoker said. "Right now, it could go either way. Right now, I just want to take it all in."
Minor League report: A few days after being taken off the seven-day disabled list, Class A Potomac outfielder Justin Maxwell has a new problem. He strained his right abdominal muscle after sneezing. Maxwell said on Monday afternoon that he is getting better and hopes to be activated in a few days.
Maxwell has been impressive this season. He hit .301 with 14 home runs and 40 RBIs for Class A Hagerstown before going to Potomac and going 7-for-17 (.412) with two RBIs.
Stat of the day: Entering Monday, the Nationals are 23-17 since starting 2007 at 9-25.
Did you know? Entering Monday's action, the Nationals are third in the National League in double plays turned with 76.
Coming up: The Nationals play the second game of a three-game series against the Braves on Tuesday at 7:35 p.m. ET at Turner Field. Washington left-hander Mike Bacsik will face Atlanta right-hander Buddy Caryle.
Bill Ladson is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.