Nava, 31, was a big part of Boston's run to the 2013 World Series title, but was hitting just .149 with two homers and three RBI when he was optioned to Triple-A Pawtucket before the game against the New York Yankees.
Wilson went 1-1 with a 4.88 ERA in 26 games with the Red Sox last year.
Boston starters were hit hard recently and manager John Farrell went to his bullpen 10 times in the past three games, forcing him to add a reliever.
''Given the number of innings by our bullpen the past four, five days, we needed to add another arm, some help out there,'' he said before Wednesday's game.
''Also, we felt like we need to find a way to get Daniel Nava going again. His struggles at the plate, I think, are evident. We're trying to get him back to seeing him be the player he has in the past.''
Batting mostly from the left side of the plate in a platoon with Jonny Gomes in left field, Nava hit a career-best .303 for Boston last year with 12 homers and 66 RBIs.
''We've got to get a guy back that was pivotal to our success last year, particularly from the left side of the plate,'' Farrell said. ''It's going to take some at-bats to do just that.''
Nava had been in the majors for a good portion of the past two seasons, so Farrell knew the news would be tough for the player.
''As you might expect, he was disappointed,'' Farrell said. ''I can't say there was disbelief. It was a disappointing message to deliver, given his role last year and the contributions. But in combination for the need for another reliever, while not liking it or deep-down agreeing with it, he knew it was a necessity.''