Puig is out of the lineup and listed as day to day for the visiting Dodgers, who will try to defeat the Washington Nationals for the sixth straight time in Monday night's opener of a three-game set.
Greinke (5-0, 2.04 ERA), looking to match his career-best 6-0 start with Kansas City in 2009, has 18 straight regular-season outings of at least five innings while allowing two or fewer runs - the longest such streak in baseball since 1914.
Puig won't be in right field behind him, having slammed into the wall chasing what turned out to be a winning RBI double in the ninth inning of Sunday's 5-4 loss at Miami. Puig was slow to walk off the field but passed a concussion test.
Andre Ethier will take Puig's place.
Puig's absence will take even more luster away from a series already missing Nationals slugger Bryce Harper, although Greinke remains enough of a draw considering how well he's been pitching.
The right-hander gave up an unearned run over six innings to earn Wednesday's 6-4 victory at Minnesota. He said he's become a much smarter pitcher than he was five years ago during his other strong season start.
"My stuff was a lot better then," Greinke said. "I'm locating better, being smarter. I've gotten a lot of help here, nice defensive plays."
Greinke is 2-0 with a 2.45 ERA in three starts against the Nationals (17-14). He also got his first career win against the Washington franchise on June 8, 2004, when it was still the Montreal Expos.
The Washington hitter he has faced the most is Denard Span, who is 9 for 31 against him.
The Dodgers have limited the Nationals to six runs and a .219 average during a five-game win streak in the series.
Washington is searching for offense after it was shut out for the second time in Sunday's 1-0 defeat at Philadelphia, going 0 for 7 with runners in scoring position.
"We've had some really key hits over the course of the season," manager Matt Williams said. "It just wasn't our day."
Nationals starter Jordan Zimmermann (2-1, 3.27) won an NL-best 12 games at home last year, but he's 0-1 with a 4.58 ERA in four starts in Washington this year compared to 2-0 with a 1.35 ERA in two on the road.
Zimmermann struck out seven in 6 1-3 innings Wednesday to cruise to a 7-0 victory over Houston.
The right-hander is 2-1 with a 6.65 ERA in four career starts against Los Angeles (18-14). Hanley Ramirez is 9 for 20 against him and Matt Kemp 5 for 12 with two homers.
Outfielder Scott Hairston (strained left oblique) and catcher Wilson Ramos (hand surgery) could both return in this series for Washington.