The comedian and actor also believes the broadcaster has a “long way” to go in promoting diversity.
The 61-year-old star made the comments in an interview with London’s Colourful Radio ahead of his appearance in the 12th series of the long-running show.
“Why have we never had a Black Doctor Who? They would rather have a dog do Doctor Who than a Black person,” Lenny said. “There’s no Black people in Doctor Who.
“When Russell T Davis was doing Doctor Who there was so many Black people in the show I rang up and said there are too many Black people in the show — put in some white people, it’s getting embarrassing.”
He added: “We’re still a long way away. The ‘in’ group who are in charge of everything are getting complacent.”
Lenny will play a tech mogul in the new series, which returns to BBC One on New Year’s Day with a two part special titled Spyfall.
Stephen Fry, Goran Višnjić, and Robert Glenister will also be making appearances in the new series.
Earlier this year, Whoopi Goldberg revealed she once pitched the idea of being the first female Time Lord, but was rejected.
The Hollywood legend wanted to take the lead in an American version of the BBC sci-fi series, long before Jodie Whittaker was announced as the first woman to take on the role last year.
Speaking on former Doctor David Tennant’s podcast, Whoopi said: “I wanted to be the first female Doctor... the American version of Doctor Who ends up in New York and it’s me.
“We don’t have a Doctor Who,” she continued. “We don’t have that character who is travelling through dimension and time, and being an observer – sometimes a hindrance, sometimes a help. The idea of that just so made me happy.”
Revealing bosses turned down her request, she added: “They were like ‘Um no.’ I was like, ‘OK, I’m cool. I understand.’”
Earlier this week, fans were given a glimpse of what to expect in an epic new trailer. Watch it below.