Greinke was supposed to start Friday but was scratched and placed on the paternity list so he could be in Los Angeles as his wife, Emily, gave birth to their son, Bode, on Thursday night.
Mattingly said the team was hopeful Greinke could catch a flight from Los Angeles to New York on Friday night, but that did not happen, eliminating him as a possible candidate to start Saturday. The Dodgers have yet to announce a starter for Saturday.
Greinke has pitched 43 2/3 consecutive scoreless innings. Former Dodgers right-hander Orel Hershiser holds the major league record with 59 straight scoreless innings.
Left-hander Ian Thomas made his first MLB start in place of Greinke on Friday night, allowing one run over five innings to pick up the win. Right-hander Josh Ravin was recalled from Triple-A Oklahoma City to fill the roster spot opened by Greinke's placement on the paternity list. He threw a scoreless ninth against New York.
Greinke, 31, is 9-2 with a 1.30 ERA this season.
In other news, Dodgers left-hander Brett Andersonthrew a bullpen session Friday afternoon and reported no pain. It is possible he will start Tuesday.
Anderson left his last start this past Tuesday with an irritated left Achilles tendon. Anderson, 27, is 5-5 with a 3.33 ERA this season.
Left fielder Alex Guerreroalso was scratched from Friday night's lineup due to back stiffness. Mattingly does not think it is anything serious, however.