Right-hander Seth Lugo will take his place as the Mets starter on Sunday.
Syndergaard complained of swelling and discomfort in his right index finger after playing catch recently.
Syndergaard last pitched on May 25, when he was pulled with 78 pitches over six innings of two-run ball due to a strained ligament in his right index finger.
The 25-year-old is 4-1 with a 3.06 ERA, 1.14 WHIP, and 76 strikeouts over 64.2 innings this season.
Lugo has been fantastic for the Mets rhis year including four scoreless innings on May 31 in a spot start. He went three scoreless innings on June 5 in relief.
The 28-year-old has a 2.04 ERA, 0.93 WHIP and has allowed only 28 hits in 39,2 innings this year.