The First Minister said it was important that any complaints against Ms Cherry were “properly considered”, but called for “due process” after several days of revelations in the media.
Ms Cherry herself accused others of “lies” and “politically-motivated smears” that “may have come from within my own party”.
SNP sources told the Scotsman at the weekend that Ms Cherry is “seen as a rival to both Nicola and Ian [Blackford] and there is a lobby within the party to discredit her”.
Addressing the row for the first time, the First Minister said she had spoken to Ms Cherry about the matter on Saturday.
“What I would say is this: firstly, Joanna is hugely talented,” Ms Sturgeon said.
“She is a massive asset to the SNP and to the Westminster parliamentary group and I think everybody recognises that.
“Secondly, where complaints are brought forward by the staff of any parliamentarian, it’s important that they’re properly considered, but that should happen under due process, not in the pages of the media.”
Asked if there was infighting within the SNP, Ms Sturgeon said: “No, I don’t think there is.
“The SNP is not just a big party, we represent a mass movement. That’s a real strength, and an attribute that most other leaders of most other parties would give their eye teeth for.
Responding to the First Minister’s words, Ms Cherry posted on twitter that she was “Pleased to have the support of Nicola Sturgeon”.
“I echo the views on the need for due process which she has today expressed,” the Edinburgh South West MP added.