The current SNP leader said the 21-year-old Paisley MP is “incredibly talented” and could lead the party “without a shadow of a doubt”, in a video interview with Elle magazine.
Ms Black pulled off one of the biggest upsets of the general election when she unseated Labour’s shadow foreign secretary Douglas Alexander and her maiden Commons speech has been watched by more than half a million people on YouTube.
She has faced criticism from opponents for her outspoken support for a second independence referendum, pledging ahead of the general election to use the power of an SNP landslide at Westminster “to twist their arm and to get that other referendum”.
Meanwhile, Ms Sturgeon has now suggested another referendum could be held after “the passage of time” as well as following a “material change” in political circumstances, and has not ruled out proposing a re-run in the next SNP manifesto.
In a separate interview with GQ, she said: “Something has to change.
“Maybe it’s just the passage of time, but it is not even a year since the last referendum; or material change, like a vote for the UK to come out of Europe but Scotland wants to stay in.
“These are things we will consider. Whether it is in the next manifesto or the one after that, we will do it based on what is right for the country.”
She said there would “undoubtedly be an appetite to look again at independence” if the UK voted to leave the European Union against Scotland’s will.
“There would have to be another referendum,” she said.
“But there would be a strong sense of fundamental change from last September that meant we had to look again, yes.”
In the Elle magazine interview, she said Ms Black “is just incredibly talented, so if she wants to then I think, yes, she could be an SNP leader”.
“Absolutely, without a shadow of a doubt,” she said.
“I don’t like piling pressure on her by saying that because people used to do that to me years and years ago, although not when I was quite as young as she is.”
Ms Sturgeon said she felt pressure to behave the same as the men around her as a young woman to get on in politics.
“There’s no particular single experience or a number of experiences,” she said.
“It was more attitudes I think, when I look back, influenced how I behaved or had to behave in politics in order to be accepted and taken seriously and to get on.
“When you’re in a very male environment as a young woman you feel the pressure to behave the way the men around you are behaving, and that then influences the way you develop and how you are perceived.
“It’s not something I was very conscious of at the time, but very conscious of looking back on it.”