The Blue Jays also received cash from San Diego. In return, the Padres get minor league right-hander Hansel Rodriguez.
Upton is batting .256 with 16 home runs, 45 RBIs and 20 stolen bases. The 12-year veteran has also played for Tampa Bay and Atlanta.
Upton is in the fourth year of a five-year, $75.25 million contract he signed with the Braves before the 2013 season. He's owed $16.45 million next season.
The 19-year-old Rodriguez is in his third season with Bluefield in the Rookie level Appalachian League. He's 2-1 with a 3.06 ERA in six starts.
Upton sat out San Diego's past two games, including Monday's 4-2 loss at Toronto. The Padres are making their first to Toronto this week.
Toronto will make a roster move to open a spot for Upton before Tuesday's game.