They went on sale at 10 a.m. ET, but just over an hour later, the team issued a news release saying that they had sold out.
The news release says that "a minimal number of tickets" are held back as a result of commitments to Major League Baseball, as well as its players and officials.
"To the extent that these tickets are returned to the club, they will be made available for public sale," the team said. Anyone eager to grab these, should they come available, will need to check the Jays website for availability.
Earlier this month, the team announced it is raising single-game ticket prices for the first time in five years. They are going up by $2.
When Toronto takes the field at Rogers Centre on April 13, fans will see a few new faces on the diamond.
Josh Donaldson will be the team's starting third baseman, after being acquired by the Jays in a November trade that sent Brett Lawrie to Oakland.
Toronto will also have some new Canadian team members taking the field. Catcher Russell Martin signed a five-year, US $82-million deal with the Jays in November. The team acquired the B.C.-born outfielder Michael Saunders in a trade with Seattle in December.
The Jays head into the 2015 season with the longest active post-season drought in baseball. They have not made the playoffs since they won their second of back-to-back World Series titles in 1993.