Conforto strained his right hamstring and McNeil strained his left in Sunday’s 7-1 loss at Tampa Bay.
“We’re taking a week-to-week approach with both of these guys,” manager Luis Rojas said.
Conforto and McNeil will remain with the Mets while receiving treatment.
Conforto said Monday he had been dealing with other injuries, including a sore calf.
“I felt like I had a good grip on all that stuff and something obviously wasn’t right going down to first base and unfortunately it grabbed on me and that’s where we’re at,” he said.
Conforto described the injury as “very, very frustrating.”
McNeil missed time last week with cramping in his leg and said Sunday the injuries might be related.
McNeil is hitting .242 with three homers and eight RBIs. Conforto is hitting .230 with two homers and 13 RBIs.
The additions of Conforto (strained right hamstring) and McNeil (strained left hamstring) increases the number of Mets starting position players on the IL to four with center fielder Brandon Nimmo (bruised left finger) and third baseman J.D. Davis (left hand sprain) currently sidelined. Mets ace Jacob deGrom (tightness in right side) also is on the injured list.
The Mets purchased the contract of Johneshwy Fargas from Triple-A Syracuse and Fargas is starting in center field in Monday night’s game at Atlanta. Fargas, 26, will be making his major league debut.
Jose Peraza is starting at second base.
“We’re very excited our depth has helped us be where we are today,” Rojas said. “We feel pretty strong about our guys coming in tonight to help us against the Braves.”
Despite the injuries, the Mets (18-16) enter Monday’s game against the Atlanta Braves with a half-game lead over the Philadelphia Phillies (21-20) in the NL East standings. Atlanta (19-21) is two games back.
The Mets also recalled outfielder Khalil Lee from Syracuse and transferred reliever Seth Lugo (elbow) to the 60-day injured list. Lugo is scheduled to make a rehab appearance with St. Lucie on Tuesday while Noah Syndergaard, who is returning from Tommy John surgery, will make a rehab appearance with St. Lucie on Wednesday.
The Associated Press contributed to this report.