He will undergo an MRI on Monday, the team said.
After failing to catch the ball, Hellickson grabbed at his right hamstring, drawing the attention of Nationals manager Davey Martinez and the team's training staff.
After a brief conversation, Martinez opted to remove Hellickson with only one out in the first inning. Hellickson was replaced by right-hander Jefry Rodriguez.
"I tried to walk, and it just kept grabbing on me,'' Hellickson said. "It's really frustrating. It's exactly what I didn't want to happen. The bullpen threw seven shutout innings yesterday and now they have to get 26 more outs. I tried to walk it off, but I couldn't.''
Albies later scored on a single by Nick Markakis.
Hellickson, 31, entered Sunday's game with a 2-0 record and a 2.30 ERA in eight starts with the Nationals this season.
Hellickson is the second starter in franchise history to throw fewer than five pitches before exiting. Dennis Martinez made one pitch for the Montreal Expos on Sept. 9, 1990, and left after getting hit in the collarbone.
ESPN's Bradford Doolittle and The Associated Press contributed to this report.