Johnson will join the Red Sox for Thursday night's game in St. Louis.
Betts, 21, is considered Boston's top prospect. He hit .244 over 13 games in two stints in the Major Leagues this season and .342 with 11 home runs, 58 RBI and 30 stolen bases over 88 games in the minors.
The Red Sox acquired Johnson, 32, at the trade deadline in a deal that sent infielder Stephen Drew and cash to the Yankees. Johnson has hit .219 with six home runs and 22 RBI over 77 games this season.
The Red Sox opened Thursday at 50-63, in last place in the American League East.
- Chris Johnson