is venturing into a whole new world of pop culture fandom with her starring role in Star Trek: Discovery
, and the actress says her time on The Walking Dead
taught her everything she needs to know about handling the attention.
"I've been calling my time on Walking Dead my sort of post-graduate degree," Martin-Green told ET's Cameron Mathison at the CBS TCA party in Los Angeles on Tuesday. "I learned so much about being on a show that has such a massive reach."
However, the 32-year-old star
says the fandom surrounding the Star Trek franchise "is on another level."
"This has expanded even beyond what I witnessed on that show," she admitted. "I've been trying to put it into words [how dedicated the fans are] and I've been kind of sort of getting it a little bit, I've been skimming the surface of how deep and profound it is to me, and how grateful and honored I truly am."
After being a main character on AMC's acclaimed horror drama for five years, Martin-Green says she's no stranger to being approached by Walking Dead fans who enjoy her work.
However, reflecting on the strangest fan encounter she's ever had, the actress admitted that it was probably the time her gynecologist recognized her from the show.
"Not in the moment. I can say, not in the moment," Martin-Green said, laughing. "It was when I was pregnant, so it was one of the pre-sit-down sort of meetings."
Despite it being a little weird, the actress said she still ended up going with that doctor during her pregnancy.
"I did the whole natural birth thing, so he was sort of on standby," she said. "But he was like, 'My sons! My sons love you!' You know? That kind of thing."
CBS announced on Tuesday during its summer Television Critics Association press tour that the first season of Star Trek: Discovery will be split into two chapters.
The first batch of episodes will run from Sept. 24 to Nov. 5, with the second returning in January 2018. The first episode will premiere on CBS and CBS All Access, before all new episodes launch weekly on the streaming service.