The 2013 NL MVP says the rules, which former owner George Steinbrenner implemented in 1973, restrict a players' self-expression.
"I definitely do think it takes away from our individualism as players and as people," McCutchen said Sunday on the "The Sports Bubble" podcast. "We express ourselves in different ways."
"I feel like maybe there should be some change there in the future - who knows when - but it's just one of the many things in this game that I feel that it needs to be talked about, it needs to be addressed," he added.
Any player suiting up for New York must not display facial hair aside from a mustache, and they need to keep scalp hair above the collar.
The five-time All-Star played with the Yankees for 25 games in 2018 following the team's late-season trade with the San Francisco Giants. He said playing for the historic franchise was an honor, but it would've been very tough for him to cut his hair if he was sporting dreadlocks, as the now the 33-year-old did earlier in his career.
"Because that was who I was," he said. "That was how I expressed myself. That's what made me Andrew McCutchen. That's how people noticed who I was, it made me unique.
"So I think, especially in this year, the year of 2020, I just feel like these things are, or should be, things that people should take at heart and realize that we have a way of expressing ourselves in different ways."