Reds manager Bryan Price said the team believes Morris' injury is a strain, and the right-hander will have his shoulder examined in Cincinnati.
Right-hander Josh Smith replaced Morris and allowed Peterson to score on an RBI single by Erick Aybar.
The Nationals selected Morris in the fourth round of the 2009 MLB Draft out of Kansas State, where he was the runner-up to Stephen Strasburg for the Golden Spikes Award.
After spending the past seven years in the Minor Leagues, Morris was promoted to Cincinnati from Triple-A Louisville on May 22. The 29-year-old made his Major League debut against the Dodgers on May 24.
In 10 innings of relief this season, Morris has allowed nine hits and seven runs while issuing eight walks and striking out nine batters.
"You've got a kid who is 29 and gets to the big leagues for the first time and is out there competing his tail off in a great opportunity tonight to go out there and pitch," Price said. "And then to have that one-pitch moment where you feel a tug, we're hoping it's just a strain.
"Strains can be very painful, as can tendinitis and some other things. [They] can all be very, very painful. So we're hoping it's nothing more than that, but we should know more by tomorrow or the following day."
Pat James is a reporter for MLB.com based in Atlanta. This story was not subject to the approval of Major League Baseball or its clubs.