Red Sox starter David Price delivers a pitch during the first inning against the Tampa Bay Rays at Fenway Park on Tuesday night. For Red Sox coverage, see Page D2.

NEW YORK — David Price’s scheduled Sunday start at Yankee Stadium is suddenly in doubt.

Price has been placed on the paternity leave list ahead of this weekend four-game series with New York. The Red Sox left-hander and his wife, Tiffany, are expecting their second child any day.

Price’s absence and the corresponding extended rest might come at an opportune time for Boston. He’s covered just 24 1/3 innings over his last five starts and recorded an out in the sixth inning only once. The Red Sox have lost in each of his last four turns through the rotation, including a 6-5 defeat against the Rays on Tuesday night.

Price has surrendered 21 hits and 13 earned runs in his last three outings, compiling an 8.16 earned-run average. Two of those starts came against Tampa Bay, who suddenly holds a 3½-game lead over the Red Sox for the second A.L. wild card spot. Boston suffered a three-game sweep against the Rays at Fenway Park and came to the Bronx on a four-game losing streak.

Price’s scheduled opponent on Sunday, Yankees left-hander J.A. Happ, was also placed on the paternity leave list Friday afternoon. Neither team has named a starting pitcher for the series finale.

Boston recalled infielder Marco Hernandez from Triple-A Pawtucket to take Price’s place on the 25-man roster. Hernandez was 14-for-35 in eight games with the PawSox after being optioned on July 23. The utility infielder was batting .339 in 27 games with the Red Sox this season, making all 12 of his starts at second base.