Mets manager Mickey Callaway said McNeil suffered a "fairly mild" left hamstring strain when trying to beat out an infield grounder in the ninth inning of Tuesday night's 5-3 loss to the Atlanta Braves.
"That is good news," Callaway said. "The bottom line is we're still going to miss him. We need some other guys to step up."
McNeil, the Mets' leadoff hitter, is batting .332 with 15 homers and 55 RBIs. This is his second IL stint with a left hamstring injury this season. He missed about two weeks, from May 23 to June 4, with his previous injury.
Callaway said it's too soon to know if McNeil might miss more than 10 days this time.
The loss of McNeil comes as New York is competing for a playoff spot. The Mets entered Wednesday's schedule two games behind St. Louis for the second NL wild card.
"I think everybody recognizes that obviously he's one of our better hitters and he gets on base," Callaway said. "He obviously led off for us. I think the nature of these guys is they won't let this bother them too much."
McNeil has been among the major league leaders in batting while providing the Mets a spark at the top of the lineup. He's played both outfield and infield, and has recently been at second base since Robinson Cano got hurt.
The 29-year-old Tejada played with the Mets from 2010 through 2015. His last major league appearance came with Baltimore in 2017. He's in the starting lineup at second base against Braves left-hander Dallas Keuchel on Wednesday night.
Right-hander Jacob Rhame was transferred to the 60-day IL. He was placed on the IL on Aug. 4 with right elbow discomfort.
Information from The Associated Press was used in this report.