The game has been rescheduled for Friday at 1:05 p.m. ET at Yankee Stadium.
Meeting in an opener for the first time since 2005, the Red Sox and Yankees had been scheduled as the first game of a Major League Baseball season pushed back from March 31 because of a 99-day lockout. With the rainout, the first game becomes the Chicago Cubs hosting the Milwaukee Brewers at Wrigley Field, a 2:20 p.m. ET start.
Seattle's game at Minnesota on Thursday also was postponed because of weather, with a mixture of rain and snow forecast.
Seven games remained on Thursday's schedule, with Brewers-Cubs joined by the New York Mets at Washington, Cleveland at Kansas City, Pittsburgh at St. Louis, Cincinnati at World Series champion Atlanta, Houston at the Los Angeles Angels and San Diego at Arizona.
The Associated Press contributed to this report.