Johnson led the Commodores in scoring (13.5) and assists (3.6) as a 6-foot-4 sophomore last season. Bright was the team's top rebounder (5.5).
Johnson said in a letter released by the university that he's been suspended "for a mistake I made, the result of using some very poor judgment." The suspension will keep the 6-foot-4 guard out for the entire 2013-14 season.
Johnson said the suspension resulted from an action that occurred near the end of the 2012-13 school year.
"It was a violation of the good conduct expected of all Vanderbilt students," Johnson said. "I take full responsibility and now must begin working to regain the trust and respect of my school, the student body, our fans and especially my coaches and friends on the team. I understand this will take time."
Johnson started all 33 games for Vanderbilt last season. He said he planned "to do everything I can" to return to Vanderbilt in time for the 2014-15 season.
Vanderbilt also announced Monday that 6-5 guard Kevin Bright has left the team to sign with the Fraport Skyliners of Frankfort, Germany. Bright made 29 starts and averaged 6.9 points to go along with 5.5 rebounds last season as a freshman from Mannheim, Germany.
Vanderbilt coach Kevin Stallings said Bright wanted to be near his ailing mother.
"About a week ago, Kevin went home to attend to his mother, who was ill," Stallings said in a statement released by the university. "Subsequently, he decided that the best thing for (him) and his family was to sign a professional contract so he could be near her. While the timing of this is very unfortunate, we understand Kevin's desire to be present for his family in this time of need.
"I do, however, look forward to working with this year's team and overcoming these recent setbacks."
Vanderbilt still returns guards Kyle Fuller and Dai-Jon Parker, who made a combined 33 starts last season as the Commodores went 16-17. Vanderbilt's backcourt also adds transfer Eric McClellan, who averaged 8.5 points, 2.5 rebounds and 2.2 assists for Tulsa in 2011-12.