Braun's spectacular 2011 season was thrown into controversy over the weekend with the news that he failed a test for a banned substance.
An official with the Baseball Writers Association of America (BBWAA), which votes for the MVP, said no action was taken on past winners who were eventually found to have used steroids.
"I got the same question after Ken Caminiti came clean about his steroids usage, and whether we should give the 1996 MVP award instead to Mike Piazza," said Jack O'Connell, longtime BBWAA secretary-treasurer and award administrator.
"The answer is no. We did not strip Alex Rodriguez of the 2003 MVP when it was learned later he used PEDs [performance-enhancing drugs] while in Texas. The voters used the information they had at the time of the election. I don't see how we can change that," he told the Times.
Dodgers outfielder Matt Kemp finished second to Braun in the MVP voting, claiming 10 first-place votes to Braun's 20.
Braun is set to appeal to MLB in an effort to avoid the automatic 50-game suspension for a failed drug test. A source told FOX Sports Sunday that the substance in question was not a PED.
The test result was highly unusual, and "never seen in the history of [baseball's] drug-prevention program," the source added.
"When it happened, everyone was just scratching their head."
Braun's first results appeared on Saturday night, saying the 28-year-old tested positive for elevated testosterone levels. Braun initially called the test result "BS," saying he learned of it in late October.
The slugger, who was drafted fifth overall by the Brewers in 2005, notched 33 home runs, 111 RBIs and 33 stolen bases last season, helping Milwaukee to 96 wins and the National League Central Division.
He was signed during the season to a five-year, $105 million extension.
Read more here