The 27-year-old Jones, who won his second career Gold Glove earlier this month, set new career highs with a .287 batting average, 32 homers, 103 runs, 186 hits, 39 doubles and 16 stolen bases.
He played in all 162 games this season. The Orioles were 23-8 in games in which Jones homered and 20 of his 32 homers either tied the game or gave the team the lead. He also hit three game-winning homers in the 12th innning or later, the first player to do that in the last 40 years.
Johnson, who recorded a club-record 51 saves, also received one third-place vote and one fourth-place vote. Wieters received a sole seventh-place vote.
Giants catcher Buster Posey won the NL MVP award after leading San Francisco to its second World Series title in the past three years.
Posey received 27 of the 32 first-place votes to beat last season's MVP, Brewers outfielder Ryan Braun, who received three first-place votes. Pirates outfielder Andrew McCutchen finished third, while Cardinals catcher Yadier Molina and Padres third baseman Chase Headley rounded out the top five.